当前课程知识点:矩阵分析(英文版) > Chapter 6 Matrix Functions > 6.2 Matrix Function via Jordan Canonical Form > Lecture 27(1)
-0.1 General Information and Course Description
-0.2 Two Practical Examples from Natural Science and Engineering
-1.1 Definitions and Examples of Linear Spaces
-1.2 Basic Facts of Linear Spaces
-1.3 Base, Dimension and Coordinate
-1.4 Subspaces and Dimension Formula
-1.5 Definitions and Examples of Linear Mappings
-1.6 Matrix Representations of Linear Mappings
-1.8 Kernels and Images of Linear Mappings, Orthogonal Complements and Four Subspaces Theorem
-2.1 Elementary Operations of λ-Matrices
-2.2 Existences of Smith Normal Forms
-2.3 Uniqueness of Smith Normal Forms
-2.4 Jordan Canonical Forms and Its Computations
-3.1 Definitions and Examples of Inner Spaces
-3.2 Schur Lemma, Normal Matrices and Its Structure Theorem
-3.3 Simultaneous Diagonalization of Normal Matrices, Hermitian Forms
-3.4 Definiteness of Hermitian Forms, Simultaneous Congruence of Pairs of Hermitian Forms
-4.1 PLU Factorization and Full Rank Factorization
-4.2 QR Decomposition
-4.3 Singular Value Decomposition
-4.4 Polar Decomposition
-4.5 Spectral Decomposition: Normal Matrices and Semisimple Matrices
-5.1 Vector Norms
-5.2 Matrix Norms
-5.3 Induced Norms and Operator Norms
-5.4 Matrix Sequences
-5.5 Matrix Series
-6.1 Matrix Polynomials and the Minimal Polynomial of A Matrix
-6.2 Matrix Function via Jordan Canonical Form
-6.3 Matrix Function via Lagrange-Hermite/Hermite Interpolating Polynomial
-6.4 Matrix Function via Matrix Series
-6.5 Matrix Function via Cauchy Integral Formula Series
-6.6 Matrix Exponential Functions and Matrix Trigonometric Functions
-7.1 Matrix-valued Functions
-7.2 Vector and Matrix Differentiation
-7.3 Linear Differential and Difference Equations
-8.1 Generalized Inverse of Matrices
-8.2 Moore-Penrose Pseudoinverses