Examination content: the concept and basic properties of determinant, and the theorem of determinant expanding by row (column).

2.[ number] matrix

Examination contents: concept of matrix, linear operation of matrix, power of matrix power, determinant of matrix product, matrix transposition, concept and properties of inverse matrix, necessary and sufficient conditions of matrix reversibility, elementary transformation of adjoint matrix, rank of elementary matrix, matrix equivalence, block matrix and its operation.

3. Understand the concept of inverse matrix, master the properties of inverse matrix and the necessary and sufficient conditions for matrix reversibility. Understand the concept of adjoint matrix and use adjoint matrix to find the inverse matrix.

4. Understand the concept of elementary transformation of matrix, understand the properties of elementary matrix and the concept of matrix equivalence, understand the concept of matrix rank, and master the method of finding matrix rank and inverse matrix by elementary transformation.

5, understand the block matrix and its operation.

6. Vector

Examination content: the concept of vector, linear combination and linear representation of vector, linear correlation of vector group has nothing to do with linearity, maximal linearity of vector group has nothing to do with, rank of equivalent vector group, relationship between rank of vector group and rank of matrix, inner product of vector, orthogonal normalization method of linear irrelevant vector group.

7, linear equations

Examination contents: Cramer's rule for linear equations, necessary and sufficient conditions for homogeneous linear equations to have nonzero solutions, necessary and sufficient conditions for nonhomogeneous linear equations to have solutions, properties and structures of solutions of linear equations, basic solution systems and general solutions of homogeneous linear equations, and general solutions of nonhomogeneous linear equations.

8. Eigenvalues and eigenvectors of matrices

Exam content: the concepts of eigenvalues and eigenvectors of matrices, the concepts and properties of similar matrices, the necessary and sufficient conditions of matrix similarity diagonalization, the eigenvalues, eigenvectors and similar diagonal matrices of real symmetric matrices of similar diagonal matrices.

9. Quadratic type

Examination contents: quadratic form and its matrix representation, contract transformation and rank of quadratic form of contract matrix, standard form and standard form of quadratic form of inertia theorem, and transforming quadratic form into standard form, quadratic form and positive definiteness of its matrix by orthogonal transformation and collocation method.

Extended data:

Common problems in linear equations and vectors are:

1, the solution of linear equations;

2. Discrimination of solution vector of equation and properties of solution:

3. Basic solution system of homogeneous linear equations;

4. The general solution structure of nonhomogeneous linear equations:

5. Common solution and identical solution of two equations.

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Research Network-19 How do candidates effectively prepare for the postgraduate entrance examination?

Research Network -20 19 Postgraduate Mathematics: Linear Algebra Combing