The course "Linear Algebra with Applications" mainly teaches the basic concepts and theorems of linear algebra. Taking Gauss elimination method for solving linear equations and solving linear equations as the breakthrough point and main line, a series of knowledge points such as matrix, determinant, vector space, orthogonality and eigenvalue, eigenvector and positive definite matrix are introduced. It focuses on the combination of basic knowledge and theory with practical application, including the application of linear algebra knowledge in web search, population migration, economic model, computer image transformation, least squares problem, spatial analytic geometry, etc. This course not only contains the basic theory of classical linear algebra, but is also close to some practical applications that we pay attention to at present.
Overview
Syllabus
- Chapter 1 - Matrices and Systems of Equations
- 1.1 Systems of Linear Equations
- 1.2 Row Echelon Form
- 1.3 Matrix Algebra
- 1.4 Elementary matrices
- 1.5 Partitioned Matrices
- Chapter 2 - Determinants
- 2.1 Determinant
- 2.2 Properties of Determinant
- 2.3 Additional Topics and Applications
- Chapter 3 Vector Spaces
- 3.1 Definition and Examples
- 3.2 Subspaces
- 3.3 Linear Independence
- 3.4 Basis and Dimension
- 3.5 Change of Basis
- 3.6 Row Space and Column Space
- Chapter 4 Linear Transformations
- 4.1 Definition and Examples
- 4.2 Matrix Representation of Linear Transformations
- 4.3 Similarity
- Chapter 5 Orthogonality
- 5.1 The Scalar Product in Rn
- 5.2 Orthogonal Subspaces
- 5.3 Least Squares Problems
- 5.6 The Gram-Schimidt Orthogonalization Process
- Chapter 6 Eigenvalues
- 6.1 Eigenvalues and Eigenvectors
- 6.3 Diagonalization
- 6.6 Quadratic Forms
- 6.7 Positive Definite Matrices
Taught by
Chao Zhang
