Equivalence (mathematics) | Matrices

Matrix similarity

In linear algebra, two n-by-n matrices A and B are called similar if there exists an invertible n-by-n matrix P such that Similar matrices represent the same linear map under two (possibly) different bases, with P being the change of basis matrix. A transformation A ↦ P−1AP is called a similarity transformation or conjugation of the matrix A. In the general linear group, similarity is therefore the same as conjugacy, and similar matrices are also called conjugate; however, in a given subgroup H of the general linear group, the notion of conjugacy may be more restrictive than similarity, since it requires that P be chosen to lie in H. (Wikipedia).

Video thumbnail

Similar matrices have similar properties

We define a notion of "Similar Matrices" where two matrices that are similar share many similar properties like eigenvalues, but don't share others like eigenvectors. This notion comes about via the idea of a change of basis Learning Objectives: 1) Apply properties of determinants to for

From playlist Linear Algebra (Full Course)

Video thumbnail

Introduction to Similarity

This video introduces similarity and explains how to determine if two figures are similar or not. http://mathispower4u.com

From playlist Number Sense - Decimals, Percents, and Ratios

Video thumbnail

60 - Similarity of matrices

Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering

From playlist Algebra 1M

Video thumbnail

Math 060 Fall 2017 102517C Matrix Representations and Similarity

Definition of linear operator. Matrix representation of a linear operator. Main question: is there a relation between the different matrix representations? Recall notion of transition matrix (between coordinate vectors). Main theorem: matrix representations of linear operators are simi

From playlist Course 4: Linear Algebra (Fall 2017)

Video thumbnail

The Similarity Relationship Represents a Change of Basis

Description: The formula P^-1AP=D is called similarity. We interpret this geometrically as being a change of basis. Learning Objective: Given two similar matrices, find a matrix that represents the transformation in the basis described by the similarity relation. This video is part of

From playlist Linear Algebra (Full Course)

Video thumbnail

What is a Matrix?

What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

Video thumbnail

Matrix addition

How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y

From playlist Introducing linear algebra

Video thumbnail

What is similarity

👉 Learn how to solve with similar triangles. Two triangles are said to be similar if the corresponding angles are congruent (equal). Note that two triangles are similar does not imply that the length of the sides are equal but the sides are proportional. Knowledge of the length of the side

From playlist Similar Triangles

Video thumbnail

61 - Properties of similar matrices

Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering

From playlist Algebra 1M

Video thumbnail

Similarity Transformation and Diagonalization

In this video we investigate similarity transformations in the context of linear algebra. We show how the similarity transformation can be used to transform a square matrix into another square matrix that shares properties with the original matrix. In particular, the determinant, eigenva

From playlist Linear Algebra

Video thumbnail

28. Similar Matrices and Jordan Form

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 28. Similar Matrices and Jordan Form License: Creative Commons BY-NC-SA More information at ht

From playlist MIT 18.06 Linear Algebra, Spring 2005

Video thumbnail

Lecture 16 - Linear Algebra Review

This is Lecture 16 of the CSE519 (Data Science) course taught by Professor Steven Skiena [http://www.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: http://www.cs.stonybrook.edu/~skiena/519 More information may be found here: http://www

From playlist CSE519 - Data Science Fall 2016

Video thumbnail

Similar Matrices

MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang If A and B are "similar" then B has the same eigenvalues as A. License: Creative Commons BY-NC-SA Mo

From playlist MIT Learn Differential Equations

Video thumbnail

4. Eigenvalues and Eigenvectors

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k Professor Strang b

From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018

Video thumbnail

WildLinAlg12: Generalized dilations and eigenvectors

This video introduces the important idea of changing coordinates in Linear Algebra. A linear transformation can be described using many different matrices, depending on the underlying coordinate system, or ordered basis, which is used to describe the space. The simplest case is when the

From playlist A first course in Linear Algebra - N J Wildberger

Video thumbnail

Linear Algebra - Lecture 34 - The Characteristic Equation

In this lecture, we discuss the characteristic equation of a square matrix. This equation is used to compute the eigenvalues for that matrix.

From playlist Linear Algebra Lectures

Video thumbnail

Matrices lesson 1 - What is a matrix, dimension of a matrix, elements of a matrix.

In this lesson we introduce you to the idea of matrices (an object containing an array of numbers). We also talk about some properties / features of matrices.

From playlist Maths C / Specialist Course, Grade 11/12, High School, Queensland, Australia

Related pages

Frobenius normal form | Algebraically closed field | If and only if | Characteristic polynomial | Linear algebra | Diagonalizable matrix | Spectral theorem | Trace (linear algebra) | Minimal polynomial (linear algebra) | Smith normal form | Diagonal matrix | Principal ideal domain | Determinant | Nilpotent matrix | General linear group | Field extension | Linear map | Elementary divisors | Change of basis | Axis–angle representation | Matrix congruence | Unitary matrix | Basis (linear algebra) | Eigenvalues and eigenvectors | Equivalence relation | Matrix equivalence | Complex number | Jordan normal form | Specht's theorem | Canonical form | Matrix (mathematics) | Permutation matrix | Rank (linear algebra) | Conjugacy class | Invertible matrix