矩阵分析（上）课程：前往报名学习
introduce the key mathematical ideas in matrix theory, which are used in modern methods of matrix Lie groups, functional analysis, data analysis, scientific computing, optimization, and merely all quantitative fields of sci-ence and engineering.
开设学校：北京理工大学；学科：理学、
introduce the key mathematical ideas in matrix theory, which are used in modern methods of matrix Lie groups, functional analysis, data analysis, scientific computing, optimization, and merely all quantitative fields of sci-ence and engineering.
-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
魏丰，现为北京理工大学数学与统计学院教授，2000年毕业于吉林大学数学系并获得理学博士学位。主要研究方向是非交换代数与非交换代数几何，有关工作和成果发表在《Advances in Mathematics》、《Forum Mathematicum》、《Journal of Algebra》、《Linear Algebra and Its Applications》、《Linear and Multilinear Algebra》、《Manuscripta Mathematica》、《Monatshefte für Mathematik》等国际数学杂志上面。先后主讲本科生“高等代数”和研究生“矩阵分析”等课程。出版中文教材一部：《矩阵分析》。先后两次获得国家留学基金委员会资助访问美国西雅图华盛顿大学（2006）和英国牛津大学（2015年）。
