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