対角化がよくわかる動画

Matrix diagonalization is a difficult concept for beginners in linear algebra. Even after memorizing the calculation method, it's common to struggle to understand the actual operation. This video aims to clearly explain the principle of diagonalization using a linear transformation on the real plane as a concrete example. Please leave any comments or suggestions in the comments section. Table of Contents 0:00 Introduction 0:29 Basis 2:50 Basis Transformation 4:30 Linear Transformation 5:34 Representation Matrix 6:58 Relationship between Linear Transformation and Representation Matrix 8:30 What are Eigenvalues ​​and Eigenvectors? 13:45 How to Find Eigenvalues ​​and Eigenvectors 20:56 What is Diagonalization? 23:00 Meaning of B=P-1AP 23:42 Not Diagonalizable 24:08 Conclusion References [1] Koji Kasahara, Linear Algebra and Eigenvalue Problems, Gendai Sugaku-sha, 2019 I'm on X (Twitter)   / hatomatzu   Correction: 5:36 The correct definition of a representation matrix is ​​f(e_j)=Σa_ij e_i (the base subscript on the right-hand side is i) Linear Algebra, Matrix, Vector Space, Linear Transformation Linear transformation, representation matrix, basis, transformation matrix, uniqueness, diagonalization, eigenvalue, eigenvector, eigenspace, diagonal matrix, eigenvalue decomposition, eigenvalue problem, similarity transformation, diagonalizable matrix, Jordan normal form, characteristic equation #LinearAlgebra #UniversityMathematics #Diagonalization