1 the second and third determinants

Total permutation and its reverse order number

Definition of 3 n-order determinant

4 exchange

5 the properties of determinant

6 determinant is expanded by row (column)

7 Cramer's rule

Exercise 1

Chapter II Matrix and Its Operation

1 matrix

2 matrix operation

3 inverse matrix

4 matrix block method

Exercise 2

Chapter III Elementary Transformation of Matrix and Linear Equations

Elementary transformation of 1 matrix

Rank of 2 matrices

3 the solution of linear equation

Exercise 3

The fourth chapter is the linear correlation of vector groups.

1 vector group and its linear combination

Linear correlation of 2 vector groups

Rank of 3 vector groups

4 Structure of Solutions of Linear Equations

5 vector space

Exercise 4

Chapter 5 Similarity Matrix and Quadratic Form

Inner product, length and orthogonality of 1 vector

Eigenvalues and eigenvectors of 2 matrices

3 similarity matrix

Diagonalization of 4 symmetric matrices

5 quadratic form and its standard form

6. Transform quadratic form into standard form by matching method.

7 positive definite quadratic form

Exercise 5

Chapter VI Linear Space and Linear Transformation

Definition and properties of 1 linear space

2 Dimensions, foundations and coordinates

3 Basic transformation and coordinate transformation

4 linear transformation

Matrix expression of 5 linear transformation

Exercise 6

The answer to the exercise