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ZL/Down/24592629/ Science and Technology Textbook/Linear Algebra and Analytic Geometry-Chen Zhizhong-Beijing Jiaotong University Press. Extension of portable document format file (abbreviation of portable document format)

Content introduction ...

Linear algebra and analytic geometry organically integrate linear algebra and spatial analytic geometry, and solve geometric problems with algebraic methods, while spatial geometry provides geometric background for algebraic theory. The book is divided into eight chapters: determinant, matrix, spatial analytic geometry, n-dimensional vector, solving linear equations, similar transformation and quadratic form, quadric surface, linear space and linear transformation, and algebraic basic theory. Each chapter is equipped with a corresponding number of examples and exercises to meet the needs of hierarchical teaching and provide mathematical basis for other courses. Linear algebra and analytic geometry is an important basic course for science, engineering and economic management in colleges and universities. Linear Algebra and Analytic Geometry can be used as a teaching material or reference book for science, engineering, economics, management and other majors in colleges and universities, and can also be used by scientific and technical personnel or self-taught personnel.

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Chapter 1 Vector and Complex Number

Linear operation of 1. 1 vector

1. 1. 1 vector and its representation

Linear operation of 1. 1.2 vector

1. 1.3 vector of * * straight line and * * plane

1.2 coordinate system

1.2. 1 affine coordinate system

Coordinate operation of 1.2.2 vector

1.2.3 Cartesian coordinate system

The product of 1.3 vector

The definition and properties of the product of 1.3. 1

Calculation of the product of quantities in Cartesian coordinate system 1.3.2

Cross product of 1.4 vector

Definition and properties of 1.4. 1 cross product

1.4.2 Calculation of Cross Product in Cartesian Coordinate System

Mixed product of 1.5 vector

1.5. 1 Definition of mixed products

Calculation of mixed product in 1.5.2 rectangular coordinate system

1.5.3 binary product

. 1.6 complex number

Four operations of 1.6. 1 complex number

Geometric representation of 1.6.2 complex number

* 1.7 number field

1.8 summation symbol

Exercise 1

Chapter II Spatial Analytic Geometry

2. 1 straight line and plane

Equation 2. 1. 1 straight line

Equation 2. 1.2 plane

2. 1.3 Distance from point to straight line

2. 1.4 Distance from point to plane

2. 1.5 positional relationship between two straight lines

2. 1.6 positional relationship between two planes

2. 1.7 positional relationship between straight line and plane

2.2 Spatial curves and surfaces

2.2. 1 curve and surface equation

cylinder

Conical surface

Rotating surface

2.2.5 introduction of quadric surface

*2.3 coordinate transformation

2.3. 1 coordinate system translation

Rotation of coordinate system

2.3.3 General coordinate transformation

Exercise 2

Chapter III Linear Equations

3. 1 Gaussian elimination method

3.2 Matrix representation of Gaussian elimination method

3.3 gauss elimination of general linear equations

3.3. 1 algorithm description

3.3.2 Properties of Solutions of Linear Equations

Exercise 3

Chapter IV Matrices and Determinants

4. 1 matrix definition

4.2 Matrix operation

4.2. 1 addition and multiplication

matrix multiplication

inverse matrix

4.2.4 Transposition, yoke and trace

block operation

fundamental transformation

4.3 determinant

4.3. Definition of1determinant

4.3.2 expansion of determinant

4.3.3 determinant calculation

cramer's rule

54.4 Grade and Balance

54.4. 1 Definition of Grade and Offset

4.4.2 Grade calculation

4.4.3 Application of migration standard format

Exercise 4

Chapter V Linear Space

5. 1 array space

5.2 Linear correlation has nothing to do with linearity

5.3 Maximum independent groups and grades

5.4 Subspaces, Basis and Dimension

5.5 Structure of Solution Set of Linear Equations

Existence and uniqueness of solutions of linear equations

5.5.2 Structure of Solution Set of Homogeneous Linear Equations

5.5.3 Structure of solution set of nonhomogeneous linear equations

5.6 General linear space

5.6. 1 Definition of General Linear Space

5.6.2 General linear space theory

*5.7 Isomorphism of Linear Space

5.8 Space and its Operation

5.8. 1 subspace

*5.8.2 Intersection of Subspaces

*5.8.3 sum of subspaces

*5.8.4 Direct sum of subspaces

Exercise 5

Chapter VI Linear Transformation

6. Definition and properties of1linear transformation

6. Definition of1.1linear transformation

6. Properties of1.2 Linear Transformation

6.2 How to carry out linear transformation

6.2. 1 Linear transformation matrix based on a set of bases

*6.2.2 One-to-one correspondence between linear transformation and matrix

*6.2.3 Operation of linear transformation

6.3 Similarity of matrices

6.3. 1 Linear transformation matrix in different bases

Similarity of matrices

6.4 eigenvalues and eigenvectors

6.4. 1 Definition of eigenvalues and eigenvectors

6.4.2 Calculation of eigenvalues and eigenvectors

6.5 Similar Diagonalization of Matrix

6.5. Necessary and Sufficient Conditions for Similarity between1Matrix and Diagonal Matrix

*6.5.2 Algebraic multiplicity and geometric multiplicity of eigenvalues

6.5.3 Similar to the upper triangular matrix

*6.6 Introduction of Jordan Standard Form

Exercise 6

Chapter 7 Euclidean space

7. 1 Definition and basic attributes

7. Definition of1.1Euclidean space

7. 1.2 Properties of Euclidean Space

7.2 Representation of Inner Product and Standard Orthogonal Basis

*7.3 Isomorphism of Euclidean Space

7.4 Linear Transformation in Euclidean Space

7.4. 1 orthogonal transformation and orthogonal matrix

7.4.2 Symmetric Transformation and Symmetric Matrix

7.4.3 Diagonalization of Real Symmetric Matrix

*7.5 subspace of Euclidean space

*7.6 Single space

7.6. Basic concepts of1unitary space

7.6.2 Basic Properties of Unitary Space

7.6.3 Unitary Transformation and Unitary Matrix

7.6.4 Hermite Transform and Hermite Matrix

7.6.5 Specification Transformation and Specification Matrix

7.6.6 Diagonalization of Unitary Transformation and Hermite Transformation

Exercise 7

Chapter VIII Real Quadratic Form

8. Matrix Representation of1Quadratic Form

8.2 the standard form of quadratic form

8.3 Uniform Invariants and Classification

8.4 Classification of Quadratic Curves and Surfaces

8.5 positive definite quadratic form

Exercise 8

* Appendix Application Case

A. static analysis of1truss

A.2 power grid analysis

A.3 Common Factor of Polynomial and Solution of Equation

A.4 combinatorial and graph theory problems

A.5 extreme value of multivariate function

A.6 computer drawing and graphic conversion

A.7 Least Square Method and Singular Value Decomposition

A.8 compression of digital images

A.9 input-output model

A. 10 Markov matrix

A. 1 1 Google search ranking

A. 12 analytic hierarchy process

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