https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 6057
MathTheBeautiful

Definitions of the vector dot product and vector length
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proving-vector-dot-product-properties?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/subspace_basis/v/linear-algebra-basis-of-a-subspace?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 658886
Khan Academy

Defining and understanding what it means to take the product of a matrix and a vector
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/null_column_space/v/introduction-to-the-null-space-of-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/matrices_elimination/v/matrices-reduced-row-echelon-form-3?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 246082
Khan Academy

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/e/scalar_matrix_multiplication?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/v/matrix-addition-and-subtraction-1?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/precalc-matrices/Basic_matrix_operations/v/data-in-matrices?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 394060
Khan Academy

Follow @mathbff on Instagram, Facebook and Twitter!

Views: 99483
mathbff

Definition of an inner and outer product of two column vectors.
Take my Coursera course at
https://www.coursera.org/learn/matrix-algebra-engineers
Download lecture notes from
http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf

Views: 4523
Jeffrey Chasnov

University of Hawaii, Dept. of Geology & Geophysics, Garrett Apuzen-Ito, GG413: Geological Data Analysis
www.soest.hawaii.edu/GG/FACULTY/ITO/GG413

Views: 2355
Garrett Apuzen-Ito

Home page: https://www.3blue1brown.com/
Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
http://3b1b.co/support
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
Various social media stuffs:
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3Blue1Brown

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! For more FREE math videos, visit http://PatrickJMT.com !!
Vectors - The Dot Product. I show how to compute the dot product of two vectors, along with some useful theorems and results involving dot products. 3 complete examples are shown.

Views: 891727
patrickJMT

This precalculus video tutorial provides a basic introduction into multiplying matrices. It explains how to tell if you can multiply two matrices together and how to determine the order of the new matrix. The order of the new matrix is based on the rows of the first matrix and the number of columns in the second matrix. To multiply two matrices together, multiply the rows of the first matrix by the columns of the second matrix and find the sum of the products. This video contains plenty of examples and practice problems on matrix multiplication.
Precalculus New Video Playlist:
https://www.youtube.com/watch?v=DrEXTC6mIO8&list=PL0o_zxa4K1BU5sTWZ2YxFhpXwsnMfMke7
Access to Premium Videos:
https://www.patreon.com/MathScienceTutor
https://www.facebook.com/MathScienceTutoring/

Views: 60536
The Organic Chemistry Tutor

Multiplying matrices example explained step by step. http://MathMeeting.com

Views: 677831
Math Meeting

Multiplying two 2x2 matrices.
Practice this yourself on Khan Academy right now: https://www.khanacademy.org/e/multiplying_a_matrix_by_a_matrix?utm_source=YTdescription&utm_medium=YTdescription&utm_campaign=YTdescription

Views: 1128809
Khan Academy

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Multiplying Matrices - Example 2. In this video, I multiply a 2 x 3 matrix by a 3 x 1 matrix.
For more free math videos, check out http://PatrickJMT.com

Views: 236687
patrickJMT

Views: 11641
Vidya Sagar

A short tutorial on multiplying 3x3 Matrices together
Keep updated with all examination walk throughs and tutorials via www.twitter.com/mathormaths and www.facebook.com/mathmathsmathematics

Views: 128081
MathMathsMathematics

Visualisation of elements in a Matrix as objects. Description of Element by Element Multiplication of Matrices (Dot Product) Using MATLAB. Written notes:
https://dellwindowsreinstallationguide.com/element-by-element-operations-multiplication/

Views: 11
Philip Yip

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
https://lem.ma/LA - Linear Algebra on Lemma
https://lem.ma/prep - Complete SAT Math Prep
http://bit.ly/ITCYTNew - My Tensor Calculus Textbook

Views: 9704
MathTheBeautiful

In this video, I go through an easy to follow example that teaches you how to perform Boolean Multiplication on matrices. This makes a confusing process easy. Feel free to comment with any remaining questions you still have, and of course I'm always open to feedback and suggested topics.
Have an integreat day!

Views: 28044
MathHacks

This lesson discusses the notations involved with the dot product, and the notation that is involved with the inner product. We will go more in depth in the actual book.

Views: 8969
JJtheTutor

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Matrices shortcuts and tricks
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Unit II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists;
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
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Mandhan Academy

Visual interpretation of the cross product and the dot product of two vectors.
My Patreon page: https://www.patreon.com/EugeneK

Views: 412566
Physics Videos by Eugene Khutoryansky

Practice this lesson yourself on KhanAcademy.org right now:
https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/e/multiplying_a_matrix_by_a_vector?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Watch the next lesson: https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/defined-and-undefined-matrix-operations?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Missed the previous lesson?
https://www.khanacademy.org/math/precalculus/precalc-matrices/matrix_multiplication/v/multiplying-a-matrix-by-a-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=Precalculus
Precalculus on Khan Academy: You may think that precalculus is simply the course you take before calculus. You would be right, of course, but that definition doesn't mean anything unless you have some knowledge of what calculus is. Let's keep it simple, shall we? Calculus is a conceptual framework which provides systematic techniques for solving problems. These problems are appropriately applicable to analytic geometry and algebra. Therefore....precalculus gives you the background for the mathematical concepts, problems, issues and techniques that appear in calculus, including trigonometry, functions, complex numbers, vectors, matrices, and others. There you have it ladies and gentlemen....an introduction to precalculus!
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to Khan Academy’s Precalculus channel:
https://www.youtube.com/channel/UCBeHztHRWuVvnlwm20u2hNA?sub_confirmation=1
Subscribe to Khan Academy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 179132
Khan Academy

how to multiply matrices is a que in mind of students.this is very simple method for begineers.
Matrices and Determinants in Most imp. Chapter for class 12 .
Matrix multiplication: Very Simple Method
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Mandhan Academy

The vector space ν with an inner product is called a (real) inner product space.
Math tutoring on Chegg Tutors
Learn about Math terms like Inner Product Spaces on Chegg Tutors. Work with live, online Math tutors like Chris W. who can help you at any moment, whether at 2pm or 2am.
Liked the video tutorial? Schedule lessons on-demand or schedule weekly tutoring in advance with tutors like Chris W.
Visit https://www.chegg.com/tutors/Math-online-tutoring/?utm_source=youtube&utm_medium=video&utm_content=managed&utm_campaign=videotutorials
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About Chris W., Math tutor on Chegg Tutors:
University of Pennsylvania, Class of 2007
Math, Computer Science major
Subjects tutored: Applied Mathematics, Geometry, Web Design, Numerical Analysis, GRE, Linear Algebra, LaTeX, Calculus, SAT II Mathematics Level 2, SSAT (math), ACT (math), Computer Science, Linear Programming, Basic Math, SAT (math), Geometry (College Advanced), Pre-Calculus, Statistics, Computer Certification and Training, Algebra, Software Engineering, Information Technology, PSAT (math), Discrete Math, Number Theory, SAT II Mathematics Level 1, Pre-Algebra, Trigonometry, and Set Theory
TEACHING EXPERIENCE
Over 7 years of experience teaching math at 3 universities and a community college. Courses ranged from Intermediate Algebra to Calculus II and class sizes varied from 2 to over 200 students. Tutoring since 2000 formally and informally, individually and in groups, for courses from Geometry to Differential Equations. Please note that I generally will not be available for audio and video in live lessons but my experience has been that audio and video aren't really needed.
EXTRACURRICULAR INTERESTS
Hiking, reading, video games, playing the guitar and piano.
Want to book a private lesson with Chris W.?
Message Chris W. at https://www.chegg.com/tutors/online-tutors/Chris-W-576966/?utm_source=youtube&utm_medium=video&utm_content=managed&utm_campaign=videotutorials
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Views: 49625
Chegg

This physics video tutorial explains how to find the cross product of two vectors using matrices and determinants and how to confirm your answer using the dot product formula. This video contains plenty of examples and practice problems using the components i j k.

Views: 79652
The Organic Chemistry Tutor

Namaste to all Friends,
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Jaipal Vishwakarma

In the "Mathematical devices in deep learning II, matrix dot product is covered

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Vasu Srinivasan

compute the product of 3x3 matrices dot product of two matrices how to multiply 3x3 matrices

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Ncert Solutions CBSE ncerthelp.com

Introduction to the cross product
Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/proof-relationship-between-cross-product-and-sin-of-angle?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Missed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/defining-a-plane-in-r3-with-a-point-and-normal-vector?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
Subscribe to KhanAcademy’s Linear Algebra channel:: https://www.youtube.com/channel/UCGYSKl6e3HM0PP7QR35Crug?sub_confirmation=1
Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy

Views: 514281
Khan Academy

Testing out this animation tool I'm making https://github.com/JonComo/anim
Starting with smaller videos, ultimately working my way towards a series on neural networks, so stick around for that! I'm going to cover everything assuming no background knowledge. It's going to be a lot to cover but I'm excited to go through it step by step and make it as understandable as I can.

Views: 7454
giant_neural_network

This is part of the Introduction to Electrodynamics series. Here, I compare the dot and cross products of two vectors from a geometric perspective.

Views: 215042
Real Physics

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Dot Product : Find Angle Between Two Vectors.
Here I do another quick example of using the dot product to find the angle between two vectors.

Views: 352593
patrickJMT

Matrices que. based on scalar matrix
Unit I: Relations and Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Unit II: Algebra
1. Matrices
Concept, notation, order, equality, types of matrices, zero and identity matrix, transpose of a matrix, symmetric and skew symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. Simple properties of addition, multiplication and scalar multiplication. Noncommutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2).Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries).
2. Determinants
Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, co-factors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix. Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix.
Unit III: Calculus
1. Continuity and Differentiability
Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. Logarithmic differentiation, derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems (without proof) and their geometric interpretation.
2. Applications of Derivatives
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).
3. Integrals
Integration as inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
syllabus 12 maths integrals
Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic propertiesof definite integrals and evaluation of definite integrals.
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
5. Differential Equations
Definition, order and degree, general and particular solutions of a differential equation.Formation of differential equation whose general solution is given.Solution of differential equations by method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:
Unit IV: Vectors and Three-Dimensional Geometry
1. Vectors
Vectors and scalars, magnitude and direction of a vector.Direction cosines and direction ratios of a vector. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors.
2. Three - dimensional Geometry
Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, shortest distance between two lines.Cartesian and vector equation of a plane.Angle between (i) two lines, (ii) two planes, (iii) a line and a plane.Distance of a point from a plane.
Unit V: Linear Programming
1. Linear Programming
Unit VI: Probability
1. Probability
Mathematics Question Papers | NCERT Books

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Mandhan Academy

Math Tutor Series for Matlab Programming.

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Ahmed Hamdy

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! In this video, I give the formula for the cross product of two vectors, discuss geometrically what the cross product is, and do an example of finding the cross product.
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patrickJMT

This video is about Linear Algebra: Matrix Multiplication and the Dot Product of a Vector

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Eva Loveland

Calculating the dot and cross products when vectors are presented in their x, y, and z (or i,j, and k) components. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/magnetic-flux-faradays-law/v/flux-and-magnetic-flux?utm_source=YT&utm_medium=Desc&utm_campaign=physics
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Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
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Khan Academy

Multiplication Of Matrices
In mathematics, matrix multiplication is the operation of multiplying a matrix with either a scalar or another matrix. This article gives an overview of the various types of matrix multiplication.
he ordinary matrix product is the most often used and the most important way to multiply matrices. It is defined between two matrices only if the width of the first matrix equals the height of the second matrix. Multiplying an m×n matrix with an n×p matrix results in an m×p matrix. If many matrices are multiplied together, and their dimensions are written in a list in order, e.g. m×n, n×p, p×q, q×r, the size of the result is given by the first and the last numbers (m×r), and the values surrounding each comma must match for the result to be defined. The ordinary matrix product is not commutative.
The element x3,4 of the above matrix product is computed as follows
The first coordinate in matrix notation denotes the row and the second the column; this order is used both in indexing and in giving the dimensions. The element at the intersection of row i and column j of the product matrix is the dot product (or scalar product) of row i of the first matrix and column j of the second matrix. This explains why the width and the height of the matrices being multiplied must match: otherwise the dot product is not defined.
The figure to the right illustrates the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. The size of the output matrix is always the largest possible, i.e. for each row of A and for each column of B there are always corresponding intersections in the product matrix. The product matrix AB consists of all combinations of dot products of rows of A and columns of B.
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TutorVista

Practice this lesson yourself on KhanAcademy.org right now: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/vectors/e/scaling_vectors?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebra
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Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
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ACCESS the COMPLETE PYTHON TRAINING here: https://academy.zenva.com/product/python-mini-degree/?zva_src=youtube-python-md
In this course we’ll be building a photo filter editor which allows you to create filters such as those used in Instagram and Snapchat. This app allows you to load a photo, edit it’s contrast, brightness and gray-scale. You can also create and apply custom filters using this tool.
Theory sections are included, where concepts such as matrices, color models, brightness, contrast and convolution are explained in detail from a mathematical perspective. Practical sections include the installation of Virtual Box, matrix operations using Numpy, OpenCV and the libraries we’ll be using. Also, the photo editor is built from scratch using OpenCV UI.
Learning goals:
Matrices
Color Models
Brightness and Contrast
Convolution
OpenCV UI
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Zenva

https://bit.ly/PG_Patreon - Help me make these videos by supporting me on Patreon!
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MathTheBeautiful

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Telusko

Home page: https://www.3blue1brown.com/
Multiplying two matrices represents applying one transformation after another. Many facts about matrix multiplication become much clearer once you digest this fact.
Full series: http://3b1b.co/eola
Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ
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3Blue1Brown

Understanding the differences between the dot and cross products. Created by Sal Khan.
Watch the next lesson: https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/calculating-dot-and-cross-products-with-unit-vector-notation?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Missed the previous lesson? https://www.khanacademy.org/science/physics/magnetic-forces-and-magnetic-fields/electric-motors/v/the-dot-product?utm_source=YT&utm_medium=Desc&utm_campaign=physics
Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.
About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.
For free. For everyone. Forever. #YouCanLearnAnything
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Khan Academy