Linear Algebra


Instructor:
Yijia Chen

Time:
8:00am - 9:40am Tuesday
9:55am - 11:35am Thursday

Textbook:
线性代数, 张巍 阚海斌 倪卫明编著 科学出版社, 2016.
勘误表.

Main References:
Linear Algebra, Gilbert Strang, MIT.
Linear Algebra, Terrance Tao, UCLA.
线性代数应该这样学, 阿克斯勒 (Sheldon Axler) (作者), 杜现昆 (译者), 刘大艳 (译者), 马晶 (译者), 人民邮电出版社, 第2版, 2016.



Lecture Notes:
(1) Sep. 15, Vectors and Vector Spaces, Matrices and Matrix Multiplication, 向量和线性空间、矩阵和矩阵乘法
(2) Sep. 17, Matrix Multiplications and Vector Subspaces, 矩阵乘法和线性子空间
(3) Sep. 22, Vector Subspaces, Linear Combinations and Spans, 线性子空间、线性组和和扩张
(4) Sep. 24, Linear Dependence, Independence, and Maximal Linear Independence, 线性相关、线性独立和极大线性独立
(5) Sep. 29, Maximal Linear Independence, Basis and Dimension, 极大线性独立、基和维数
(6) Oct. 10, Steinitz Exchange Lemma, Matrices and Block Matrices, Steinitz交换引理、矩阵和分块矩阵
(7) Oct. 13, Elementary Operations, Elementary Matrices, Row and Column Ranks, 初等变换、初等矩阵,矩阵的行秩和列秩
(8) Oct. 15, Matrix Rank and Elementary Operations, Row Echelon Form and Reduced Row Echelon Form, 矩阵的秩和初等变换,阶梯形和最简阶梯形
(9) Oct. 20, Systems of Linear Equations, 线性方程组
(10) Oct. 22, Solutions of Ax=b, Matrix Inverse, Ax=b的解,逆矩阵
(11) Oct. 27, Matrix Inverse, Determinants, 逆矩阵,行列式
(12) Oct. 29, Determinants, and Computing Determinant by Any Row, 行列式,由任意行展开计算行列式
(13) Nov. 3, Computing Determinant by Any Column, 由任意列展开计算行列式
(14) Nov. 5, Properties of Determinant, Adjugate Matrix, 行列式的性质,伴随矩阵

Nov. 10 Midterm

(15) Nov. 12, Cramer's Rule, Linear Transformation, Cramer法则,线性变换
(16) Nov. 17, Transition Matrix, Linear Transformation and Representation Matrix, 过渡矩阵,线性变换和表示矩阵
(17) Nov. 19, Matrix Similarity, Kernels and Images, 矩阵相似性,线性映射的核和像
(18) Nov. 24, The Rank-Nullity Theorem, Intersection and Sum of Subspaces, 秩 — 零空间定理、线性空间的交与和
(19) Nov. 26, Direct Sum of Subspaces, 子空间的直和
(20) Dec. 1, Inner Product Spaces, Orthogonal Bases, 内积空间,正交基
(21) Dec. 3, Gram-Schmidt Process, Orthogonal Complement and Least Squares Approximation, Gram-Schmidt正交化,正交补空间和最小二乘解
(22) Dec. 8, Least Squares Approximation, Orthogonal Transformation, Eigenvalue and Eigenvector, 最小二乘解,正交变换,特征值和特征向量
(23) Dec. 10, Eigenvalue and Eigenvector, Algebraic and Geometric Multiplicity, 特征值和特征向量,代数重数和几何重数
(24) Dec. 15, Linear Independence of Eigenvectors, Matrix Diagonalization, 特征向量的线性独立性,矩阵对角化
(25) Dec. 17, Real Symmetric Matrices, 实对称矩阵
(26) Dec. 22, Quadratic Form and Positive Definite Matrices, 二次型和正定矩阵
(27) Dec. 24, Matrix Decompositions, 矩阵分解


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Yijia Chen, last modified: 14. 12. 2020