Linear Algebra


Instructor:
Yijia Chen

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

Textbook:
高等代数学(第3版), 姚慕生 , 吴泉水 , 谢启鸿 , 复旦大学出版社, 2014.


Main Reference:
Linear Algebra, Terrance Tao.


Lecture Notes:
(1) 11/09 (Vectors and Vector Spaces)
(2) 13/09 (Linear Combination and Linear Independence)
(3) 18/09 (Maximal Linear Independence)
(4) 20/09 (Rank, Bases, and Dimension)
(5) 25/09 (Isomorphisms and Isomorphic Vector Spaces)
(6) 27/09 (Subspaces)
(7) 29/09 (Dimension of Subspaces)
(8) 09/10 (Direct Sum of Subspaces)
(9) 11/10 (Matrices and Matrix Operations)
(10) 16/10 (More Matrix Operations)
(11) 19/10 (Elementary Operations, Row and Column Ranks)
(12) 23/10 (Matrix Rank)
(13) 25/10 (Matrix Inverse, Rank, and Elementary Matrices)
(14) 30/10 (Matrix Inverse by Elementary Operations)
(15) 01/11 (Block Matrices and 2*2 Determinants)
(16) 08/11 (Determinants and Their Properties)
(17) 11/11 (Properties of Determinants and Cramer's Rule)
(18) 13/11 (Matrix Adjugate and Inverse, Matrix Multiplication and Determinants, Vandermonde Matrices )
(19) 15/11 Midterm
(20) 20/11 (Vandermonde Matrices, Base Change and Transition Matrices, and Solutions of Ax=b)
(21) 22/11 (Solutions of Ax=b)
(22) 27/11 (Linear Maps and Representation Matrices)
(23) 29/11 (Linear Maps and Bases, Images and Kernels)
(24) 04/12 (The Rank-Nullity Theorem, Eigenvalues, and Eigenvectors)
(25) 06/12 (Eigenvalues, Eigenvectors, and Diagonalizable Matrices)
(26) 11/12 (Diagonalization)
(27) 13/12 (Diagonalization and Quadratic Forms)
(28) 18/12 (Sylvester's Law of Inertia and Positive Definiteness)
(29) 20/12 (Positive Definiteness and Leading Principal Minors)
(30) 24/12 (Inner Product Spaces, Orthogonal Bases, and Real Symmetric Matrices)
(31) 27/12 (Diagonalization of Real Symmetric Matrices, Singular-Value Decompositions, and Least Squares Approximations)


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Yijia Chen, last modified: 08. 01. 2019