Course Content and Requirements

Lecture 1: Matrices（6 hrs）

This lecture will introduce basic definitions of matrices and some special matrices. Students should be able to understand the fundamental of matrices and master the structures and properties of special matrices.

Lecture 2: Matrix Operations（8 hrs）

This lecture will introduce basic operations of matrices. Students should be able to understand the basic operations of matrices and master the applications of matrix operations.

Homework: Some exercises on matrix operations after class.

Lecture 3: Matrix Transposition and Related Topics（8 hrs）

This lecture will introduce matrix transposition and related topics on applications. Students should be able to understand the basic definitions and properties of matrix transposition and master the applications of matrix transposition in related matrix operations and advanced matrix computation.

Homework: Some exercises on applications in matrix splitting after class.

Lecture 4: Matrix Inversion（8 hrs）

This lecture will introduce matrix inversion and investigate Sherman-Morrison-Woodbury formula with its applications in finding the inverse of a partitioned matrix. Students should be able to understand the basic definitions and properties of matrix inverse and master the applications of Sherman-Morrison-Woodbury formula.

Lecture 5: Special Matrices Again（6 hrs）

This lecture will introduce unitary and orthogonal matrices, and particularly study two special cases as Givens rotation and permutation matrix. Students should be able to understand the basic contents of unitary and orthogonal matrices and to master the applications of these special matrices.

Homework: Some exercises on permutation matrices after class.

Lecture 6: Special Matrices Again（4 hrs）

This lecture will introduce triangular matrices with applications in matrix factorization. Students should be able to understand the basic properties of triangular matrices and to master their applications in matrix factorization.

Homework: Some exercises on special matrices after class.

Lecture 7: Sensitivity（2 hrs）

This lecture will introduce sensitivity and conditioning with some background and examples. Students should be able to understand the significance of such topic and to master the sensitivity theory in matrix operations.

Lecture 8: Errors（2 hrs）

This lecture will introduce importance of errors and the computing environment. Students should be able to understand the importance of such errors and to master how to characterize the errors.

Lecture 9: Vector Norm（4hrs）

This chapter will introduce concepts and properties of vector norms and some important inequalities.

Lecture 10: Matrix Norm（6 hrs）

This chapter will introduce concepts and properties of matrix norms and some special induced matrix norms.

Lecture 11: Conditioning of Matrix Operations（6 hrs）

This chapter will study conditioning of matrix operations and conditioning of matrix inversion.