Each chapter of the book gives the basic concepts, basic principles and basic properties that need to be mastered according to the system, with special emphasis on the summary of the relationship between properties; On the basis of understanding the basic concepts, principles and properties, each part gives typical comprehensive questions, classifies and summarizes according to the questions, and gives normative and detailed answers; Each part provides exercises for readers to check and master. The types of questions are comprehensive, which are very useful for improving the examinees' computing ability and their ability to skillfully use basic principles to solve problems. Bibliography:
Chapter I Determinant
Summary of this chapter
Explanation of important knowledge points
Section 1 Basic concepts and properties of determinant
Section II Application of Determinant Kramer's Law
integrated question
Basic concepts of one determinant of question type
Calculation of the second lower order determinant of the question type
Calculation of the third n-order determinant of the question type
The Determinant Calculation of Four Matrices
Five cofactor and algebraic cofactor
Exercises in this chapter
Answers and analysis of exercises
Chapter 2 Matrix
Summary of this chapter
Explanation of important knowledge points
Section 1 Basic Concept of Matrix and Special Matrix
Section 2 Operation and Properties of Matrix
Section 3 Inverse Matrix of Matrix
Section 4 Rank of Matrix
Section 5 Matrix Equivalence
integrated question
Question 1: Operation of matrix and calculation of determinant of matrix (continued)
Power matrix of two matrix of question type
Three Elementary Transformations and Elementary Matrices
Calculation and Proof of Four Inverse Matrix
The relationship between the five adjoint matrix and the inverse matrix of the matrix
Six matrix equation
Rank of question type seven matrix
Exercises in this chapter
Answers and analysis of exercises
Chapter 3 Vector
Summary of this chapter
Explanation of important knowledge points
Section 1 The concept and operation of vector
Section 2 Correlation and linear representation of vector groups
Section 3 Vector group equivalence, maximum linear independence group of vector group and rank of vector group
Section 4 n-dimensional vector space (only for Math 1)
integrated question
Correlation of question type vector group
Linear representation of two vectors for question types
The Equivalence of Three Vector Groups and the Rank of Vector Groups
Item 4 Coordinates of transition matrix and vector (only for Math 1)
Exercises in this chapter
Answers and analysis of exercises
Chapter IV Linear Equations
Summary of this chapter
Explanation of important knowledge points
integrated question
The Theoretic Proof of the Solution of a System of Equations
The Structure and Properties of Solutions of Bilinear Equations
The Solution of Three Homogeneous Linear Equations
General Solution of the Problem Type Four Nonhomogeneous Linear Equations
The common solution of the problem type five equation system and the same solution of the equation system
Exercises in this chapter
Answers and analysis of exercises
Chapter V Eigenvalues and Eigenvectors
Summary of this chapter
Explanation of important knowledge points
Section 1 Basic concepts of eigenvalues and eigenvectors
Section 2 Properties of eigenvalues and eigenvectors
Section 3 Matrix Diagonalization Theory
integrated question
Question 1 Finding the eigenvalues and eigenvectors of matrices
Definition and properties of eigenvalues and eigenvectors of question type 2
Judgment on Similarity of Three Matrices
Diagonalization of the four non real symmetric matrices
Diagonalization of Five Real Symmetric Matrices
Type 6 Am
Finding unknown matrix by eigenvalue method of question type 7
The Proof of Eigenvalue and Eigenvector Proposition of Item 8
Exercises in this chapter
Answers and analysis of exercises
Chapter VI Quadratic
Summary of this chapter
Explanation of important knowledge points
Section 1 Basic concepts of quadratic form and its canonical form
Section 2 Positive Definite Matrix and Positive Definite Quadratic Form
integrated question
Concept and nature of primary and secondary question types
The canonical form of the quadratic form of the question type
Quadratic problems with three parameters
Discrimination and Proof of Quadratic Positive Definite Questions
Five matrix similarity and contract
Exercises in this chapter
Answers and analysis of exercises
