Chapter 1 of Linear Algebra: Determinant Examination Content: The concept and basic properties of determinant. The determinant is expanded by rows (columns). Examination requirements: 1. Understand the concept of determinant. Master the nature of determinant. 2. Calculate the determinant by applying the properties of determinant and the theorem of its expansion in rows (columns). Chapter 2: Matrix test contents: the concept of matrix, the concept of matrix, the inverse matrix of multiplication matrix, the necessary and sufficient conditions for the reversibility of property matrix, the elementary transformation of adjoint matrix, the rank matrix equivalent block matrix of elementary matrix and its operation test requirements; 1. Understand the concepts and properties of matrix, identity matrix, quantitative matrix, diagonal matrix, triangular matrix, symmetric matrix and antisymmetric matrix. 2. Master the linear operation, multiplication, transposition and its operation rules of matrix, and understand the properties of matrix multiplied by determinant of matrix. 3. Understand the concept, properties and necessary and sufficient conditions of inverse matrix, and understand the concept of adjoint matrix. Will use the adjoint matrix to find the inverse matrix. 4. Understand the concept of matrix elementary transformation, the properties of elementary matrix and the concept of matrix equivalence, and the concept of matrix rank. Master the method of finding the rank and inverse matrix of matrix by elementary transformation. 5. Understand the block matrix and its operation. Chapter 3: The contents of vector examination: the linear combination of concept vectors of vectors and the linear representation of linear correlation of vector groups and the maximum linear independence of linear independent vector groups, the relationship vector space between the rank of rank vector groups and the rank of matrix, the basic transformation of related concept N-dimensional vector space and coordinate transformation to transform matrix vectors. Orthogonal normalization method of inner product linear independent vector group based on standard orthogonal matrix and its property test requirements: 1. Understand the concepts of n-dimensional vector, linear combination of vectors and linear representation. 2. Understand the concepts of linear correlation and linear independence of vector groups, and master the related properties and discrimination methods of linear correlation and linear independence of vector groups. 3. Understand the concepts of maximal linear independent group of vector group and rank of vector group. Will find the maximum linearly independent group and rank of vector group. 4. Understand the concept of vector group equivalence and the relationship between the rank of matrix and the rank of its row (column) vector group. 5. Understand the concepts of N-dimensional vector space, subspace, basis, dimension and coordinates. 6. Understand the formulas of base transformation and coordinate transformation, and find the transfer matrix. 7. Understand the concept of inner product. Master the Schmidt method of orthogonal normalization of linear independent vector groups. 8. Understand the concepts and properties of normalized orthogonal basis and orthogonal matrix. Chapter four: the examination content of linear equations: the necessary and sufficient conditions for homogeneous linear equations to have non-zero solutions; Necessary and sufficient conditions for non-homogeneous linear equations to have solutions: properties and structure of solutions; The basic solution system of homogeneous linear equations and the general solution requirements of non-homogeneous linear equations in the general solution space; L. can use clem's law; 2. got it. Necessary and sufficient conditions for homogeneous linear equations to have nonzero solutions and nonhomogeneous linear equations to have solutions. 3. Understand the basic solution system, general solution and solution space of homogeneous linear equations. Master the basic solution system of homogeneous linear equations and the solution method of general solution. 4. Understand the structure of solutions of nonhomogeneous linear equations and the concept of general solutions. 5. Master the method of solving linear equations with elementary line transformation. Chapter 5: Examination contents of eigenvalues and eigenvectors of matrices: the concepts of eigenvalues and eigenvectors of matrices, the transformation of similarity properties, the necessary and sufficient conditions for similarity diagonalization, and the examination requirements for eigenvalues, eigenvectors and similar diagonal matrices of real symmetric matrices of similar diagonal matrices are: 1. Understanding the concepts and properties of eigenvalues and eigenvectors of matrices will help you find eigenvalues and eigenvectors of matrices. 2. Understand the concept and properties of similar matrix and the necessary and sufficient conditions for similar diagonalization of matrix, and master the method of transforming a matrix into similar diagonal matrix. 3. Master the properties of eigenvalues and eigenvectors of real symmetric matrices. Chapter 6: Quadratic test content: Quadratic and its matrix represent the rank inertia theorem of contract transformation and the quadratic form of contract matrix. Through orthogonal transformation and configuration, the standard form and canonical form of quadratic form are transformed into standard quadratic form and its matrix. Positive definite test requirements: 1. Master quadratic form and its matrix representation, understand the concepts of quadratic form's rank, contract transformation and contract matrix, and the concepts of quadratic form's standard form, standard form and inertia theorem. 2. Master the method of transforming quadratic form into standard form by orthogonal transformation, and use collocation method to transform quadratic form into standard form. 3. Understand the concepts of positive definite quadratic form and positive definite matrix, and master their discrimination methods.