Linear Algebra Lecturer Xia Liao Email xliaohqu edu
Linear Algebra Lecturer: Xia Liao Email: xliao@hqu. edu. cn Homepage: https: //hirzebruch. github. io/main. html Time: every Tuesday 1 -2, Thursday 3 -4
A need for fast solving systems of linear equations The working process of CFD involves repeatedly solving a system of linear equations which contains up to 2 million variables.
Matrix notations •
Matrix notations •
Equality of matrices •
Sum of two matrices •
Scalar multiples
Relation between matrix addition and scalar multiplication
Matrix multiplication
Matrix multiplication •
Matrix multiplication
Matrix multiplication •
The computation of the matrix product
The computation of the matrix product
The computation of the matrix product •
The computation of the matrix product
The computation of the matrix product •
Properties of matrix multiplication
Properties of matrix multiplication Proof of (a):
The associativity of the matrix product •
Non-commutativity of matrix product •
The difference between matrix algebra and the ordinary algebra of real numbers P 108: Exercise 9 -12
The difference between matrix algebra and the ordinary algebra of real numbers
Powers of a matrix •
Powers of a matrix P 110: Exercise 40
The transpose of a matrix
The properties of matrix transpose
practice P 108: 1, 2, 5, P 109: 15 -25, 29 -32
- Slides: 34