Chapter 1 Determinants Section 1: Second-order and Third-order Determinants Section 1: Second-order Determinants Section 2: Arrangement and Inverse Order Section 1: Number of Arranged Inverse Orders Section 2: Definition of Sequential Determinants Section 4: Properties of Sequential Determinants Section 5: Determinants are expanded by rows (columns) Section 6: Exercise 1: Chapter 2: Matrices Section 1: Concepts of Matrices Section 2: Matrix Operations. Multiplication three of matrix, transposition four of matrix. The power of a square matrix. Several special matrices I, diagonal matrix II, quantitative matrix III, identity matrix matrix IV, triangular matrix V and symmetric matrix IV. Elementary transformation of inverse matrix v. Rank of matrix VI. Partition of matrix II. Chapter three. Elimination method of linear equations linear correlation of vector groups in in n-dimensional vector space III. Linear combination II. Linear correlation is independent of linearity. 3. Currency relativity theorem of vector group. 4. Rank 5 of vector group, basis and dimension of vector space. Section 4. Structure of solutions of linear equations. Section 2. Structure of solutions of nonhomogeneous linear equations. Exercise 3. Orthogonal normalization of the first similar matrix and quadratic form of symmetric matrix and the second quadratic form. Section 3. Eigenvalues and eigenvectors of similar matrices. Section 5. Diagonalization of real symmetric matrices. Section 6. Quadratic form is standard.