In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied. Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if is a square matrix representing a rotation (rotation matrix) and is a column vector describing the position of a point in space, the product yields another column vector describing the position of that point after that rotation. If is a row vector, the same transformation can be obtained using , where is the transpose of . (Wikipedia).
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
The Diagonalization of Matrices
This video explains the process of diagonalization of a matrix.
From playlist The Diagonalization of Matrices
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
(3.2.3) The Determinant of Square Matrices and Properties
This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Invertible matrices are square
Why invertible matrices must be square. Definition of invertible matrix and showing that a 3x2 and a 2x3 matrix cannot be square. Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0 Subscribe to my channel: https://www.youtube.c
From playlist Matrix Algebra
Matrices: Inverse of 2x2 and 3x3 Matrix
This is the sixth video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with finding the inverse of a square 2x2 or 3x3 matrix. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Matrices
This video introduces the identity matrix and illustrates the properties of the identity matrix. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Introduction to Matrices and Matrix Operations
Linear Algebra 23b: How to Determine the Matrices Q and S in the Polar Decomposition
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From playlist Part 3 Linear Algebra: Linear Transformations
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3)
Lie Groups and Lie Algebras: Lesson 29 - SO(3) from so(3) In this video lesson we construct the Lie group elements of SO(3) starting from the defining property of SO(3) and the Lie algebra of so(3). To do this we review the Caley-Hamilton theorem that a square matrix satisfies its own cha
From playlist Lie Groups and Lie Algebras
Linear Algebra 22f: Symmetric Matrices and the Eigenvalue Decomposition
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From playlist Part 3 Linear Algebra: Linear Transformations
Determine the Singular Value Decomposition of a Matrix
This video explains how to determine the singular value decomposition of a matrix.
From playlist Singular Values / Singular Value Decomposition of a Matrix
Determine the Singular Value Decomposition of a Matrix
This video explains how to determine the singular value decomposition of a matrix. https://mathispower4u.com
From playlist Singular Values / Singular Value Decomposition of a Matrix
26. Complex Matrices; Fast Fourier Transform
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 26. Complex Matrices; Fast Fourier Transform License: Creative Commons BY-NC-SA More informati
From playlist Fourier
In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im
From playlist Complex Numbers
The LDU and LDLᵀ Decompositions and the Implications for Positive Definiteness
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Linear Algebra 22j: The Cholesky Decomposition and a Tribute to Land Surveyors
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From playlist Part 3 Linear Algebra: Linear Transformations
A more in depth discussion on the determinant of a square matrix.
From playlist Linear Algebra
Lec 29 | MIT 18.03 Differential Equations, Spring 2006
Matrix Exponentials; Application to Solving Systems. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 18.03SC Differential Equations, Fall 2011