introduce

0. 1 overview

0.2 preparation

Chapter 65438 +0 polynomial

1. 1 number field

1.2 unary polynomial

1.3 divided by the remainder

1.4 Maximum common factor

1.5 factorization

1.6 derivative, multiple factor

The root of 1.7 polynomial

1.8 rational coefficient polynomial

1.9 Multivariate Polynomial

1. 10 cases

Chapter II Determinants

2. 1 matrix

2.2 determinant

2.3 the nature of determinant

2.4 Complete expansion of determinant

2.5 Cramer's Law

2.6 cases

Chapter III Matrix

3. 1 matrix operation

3.2 invertible matrix

3.3 matrix block

3.4 Elementary Transformation of Matrix and Elementary Matrix

3.5 Matrix and Linear Equation

3.6 cases

Chapter 4 Linear Space

4. 1 vector and its linear operation

4.2 coordinate system

4.3 Definition of Linear Space

4.4 Linear correlation, linear independence

4.5 Levels, Dimensions and Foundations

4.6 Rank of Matrix

4.7 linear equation

4.8 Coordinate and Basic Transformation

4.9 Subspace

4. 10 quotient space

4. Homomorphism and Isomorphism of11Linear Space

Basic Theorem of Appendix Algebra

Index of the first volume

Higher Algebra and Analytic Geometry: Volume II

Chapter V Linear Transformation

5. Definition of1linear transformation

5.2 Operation of Linear Transformation

5.3 Linear transformation matrix

5.4 Eigenvalues and Eigenvectors

5.5 Linear Transformation with Diagonal Matrix

5.6 invariant subspace

5.7 Second, the linear transformation of three-dimensional complex linear space

5.8 canonical form of linear transformation in complex linear space

Chapter VI Polynomial Matrix

6. 1 Polynomial Matrix and Its Paradigm

6.2 Uniqueness of standard form

6.3 Conditions of Matrix Similarity

6.4 Jordan canonical form of compound array

Chapter 7 Euclidean space

7. Definition of1Euclidean space

7.2 standard orthogonal basis

7.3 Isomorphism of Euclidean Space

7.4 Subspace

7.5 *** yoke conversion, normal conversion

7.6 orthogonal transformation

7.7 Symmetric transformation

7.8 unitary space and its transformation

7.9 Cross products and mixed products

Chapter 8 Bilinear Functions and Quadratic Forms

8. 1 dual space

8.2 bilinear function

8.3 Quadratic form and its standard form

8.4 uniqueness

8.5 positive definite quadratic form

8.6 Application of Quadratic Form in Analysis

8.7 Application of Quadratic Form in Analytic Geometry

Chapter 9 quadric surface

9. 1 quadric surface

9.2 ruled surface

9.3 Rotating surface

9.4 Affine Properties of Quadratic Surfaces

9.5 Metric Properties of Quadratic Surfaces

Chapter 10 Affine Geometry and Projective Geometry

10. 1 affine geometry

Basic affine properties of 10.2

10.3 affine isomorphism

The basic theorem of 10.4 affine geometry

10.5 projective geometry

Basic related theorems of 10.6 projective geometry

10.7 projective isomorphism

10.8 double geometry

10.9 projective quadratic form

refer to

Index of next volume