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.


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) 10/09 (Vector and Vector Space)
(2) 12/09 (Matrix Multiplication and Vector Subspace)
(3) 17/09 (Vector Subspace, Linear Span and Combination)
(4) 19/09 (Linear Dependence)
(5) 24/09 (Maximal Linear Independence)
(6) 26/09 (Rank, Basis and Dimension)
(7) 08/10 (Steinitz Exchange Lemma, Matrix and Block Matrix)
(8) 10/10 (Elementary Operations, Elementary Matrices, Row and Column Ranks)
(9) 15/10 (Matrix Rank and Elementary Operations)
(10) 17/10 (Systems of Linear Equations)
(11) 22/10 (Solutions of Ax=b and Matrix Inverse)
(12) 24/10 (Matrix Inverse and Determinant)
(13) 29/10 (Determinant)

31/10 Midterm

(14) 07/11 (Computing Determinant by any Row)
(15) 09/11 (Computing Determinant by any Column)
(16) 12/11 (Properties of Determinant and Adjugate Matrix)
(17) 14/11 (Cramer's Rule, Vector Space and Linear Transformation)
(18) 19/11 (Transition Matrix, Linear Transformation and Representation Matrix)
(19) 21/11 (Matrix Similarity, Kernel and Image)
(20) 26/11 (The Rank-Nullity Theorem, Intersection and Sum of Subspaces)
(21) 28/11 (Direct Sum of Subspaces, Inner Product Space)
(22) 03/12 (Gram-Schmidt Process, Orthogonal Complement and Least Squares Approximation)
(23) 05/12 (Orthogonal Transformation, Eigenvalue and Eigenvector)
(24) 10/12 (Eigenvalue and Eigenvector, Algebraic and Geometric Multiplicity)
(25) 12/12 (Linear Independence of Eigenvectors, Matrix Diagonalization)
(26) 17/12 (Real Symmetric Matrix and Quadratic Form)
(27) 19/12 (Quadratic Form and Positive Definite Matrix)
(28) 24/12 (Matrix Decompositions)


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Yijia Chen, last modified: 23. 12. 2019