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Linear algebra Chapter 2 - matrices and their operations

2022-04-23 05:58:00 【＃self-discipline＃】

System of linear equations

n A system of nonhomogeneous linear equations ：

n A system of homogeneous linear equations ：

Definition of matrix

Matrix operations

Matrix addition

Matrix number times

The rules

Matrix Matrix Multiplication

The rules

from （iii） It can be seen that the multiplication of matrices satisfies the distribution law

characteristic

1. Non commutativity of matrix multiplication ：

2. From rotation and matrix multiplication ：

Matrix transposition

The rules

The determinant of a square

The rules

characteristic

, among

Inverse matrix

Operational rules

Preliminary application of inverse matrix

Calculation A The polynomial $\phi(A)$

1. structure $A=P\Lambda P^{-1}$ , among $\Lambda =diag(\lambda_1,\lambda_2,...,\lambda_n)$ For diagonal matrix

2. Yes $\Lambda^k =diag(\lambda_1^k,\lambda_2^k,...,\lambda_n^k)$ , solve $\phi(\Lambda )$ obtain $\phi(A)$

Kramer's law

Matrix block method

Operational rules

1.

2.

3.

4.

5.

characteristic

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