Syllabus

Instructor: Yu Yi Email: yuyi2019@pku.edu.cn

Textbook: Introduction to Linear Algebra, Fifth Edition (2016)

Textbook open resource: http://math.mit.edu/~gs/linearalgebra/

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Content

Part I

Lecture 1 Introduction of Linear Algebra

Lecture 2 Linear Equation

Lecture 3 Rules for Matrix Operation

Lecture 4 Gauss-Jordan Elimination and Factorization

Lecture 5 Vector Space

Lecture 6 Four subspaces of a matrix

Lecture 7 Orthogonality

Lecture 8 Determinants

Lecture 9 Basis (4.4, 5.3)

Part II

Lecture 10 Eigenvalue and Eigenvector

Lecture 11 Symmetric Matrix

Lecture 12 Positive Definite Matrix

Lecture 13 Simillar Matrix

Lecture 14 Jordan Form

Lecture 15 Linear Transformation (I)

Lecture 16 Linear Transformation (II)

Part III

Lecture 17 Complex vectors and Matrix(Shur Theorem P335)

Lecture 18 Markov Matrix

Lecture 19 Differential Equation

Lecture 20 High Dimensional Calculus