The first chapter determinant
First, the examination outline requirements
Second, the basic content and important conclusions
The form and significance of 1. 1
1.2 definition (fully extended)
1.3 attribute
1.4 calculation
1.5 Cramer rule
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Chapter II Matrix Multiplication and Reversible Matrix
First, the examination outline requirements
Second, the basic content and important conclusions
2. Definition and properties of1matrix multiplication
Power sum polynomial of 2.2-order matrix
2.3 column vector group and row vector group of product matrix
2.4 Matrix Equation and Reversible Matrix (Adjoint Matrix)
2.5 Block Rules of Matrix Multiplication
2.6 elementary matrix
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Chapter 3 Linear Relation and Rank of Vector Groups
First, the examination outline requirements
Second, the basic content and important conclusions
3. Linear Representation of1Vector Group
3.2 Linear Correlation of Vector Groups
3.3 Maximum Independent Groups and Ranks of Vector Groups
3.4 Calculation of Rank and Maximum Irrelevant Group of Vector Groups with Same Linear Relationship
3.5 Rank of Matrix
3.6 Matrix Equivalence
3.7 Real Vector Inner Product of Orthogonal Matrix and Schmidt Orthogonalization
3.8 vector space
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Chapter IV Linear Equations
First, the examination outline requirements
Second, the basic content and important conclusions
4. 1 Form of linear equations
4.2 Form of solution of linear equations
4.3 Discrimination of Solutions of Linear Equations
4.4 Basic solution system of homogeneous equations and general solution of linear equations
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Chapter 5, eigenvectors and eigenvalues, diagonalization
First, the examination outline requirements
Second, the basic content and important conclusions
5. 1 eigenvectors and eigenvalues
5.2 Similarity and Diagonalization
5.3 Diagonalization of Real Symmetric Matrix
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Chapter VI Quadratic Form and Positive Form
First, the examination outline requirements
Second, the basic content and important conclusions
6. 1 quadratic form and its matrix and reversible linear change substitution
6.2 Standardization and normalization of quadratic form
6.3 positive definite quadratic form and positive definite matrix
Third, the typical case analysis
Fourth, self-test exercises and reference answers
Appendix 1 the relationship between the solution sets of two linear equations
Appendix 2 2006 National Unified Entrance Examination for Postgraduates Mathematical Questions Linear Algebra Questions and Solutions
Appendix 3 2007 National Unified Entrance Examination for Postgraduates Mathematical Questions Linear Algebra Questions and Solutions
Appendix 4 Linear Algebra Test Questions and Solutions of Mathematics in 2008 National Unified Entrance Examination for Postgraduates
Appendix 5 2009 National Unified Entrance Examination for Postgraduates Mathematical Questions Linear Algebra Questions and Solutions