1. Learning and Understanding of Advanced Algebra
2. In advanced algebra. . . . think
3. In advanced algebra. . . . way
4. The relationship between higher algebra and analytic geometry.
5. Equivalence proposition of related theories of higher algebra.
6. Geometric description of related theories of higher algebra.
7. Application examples of related theories of advanced algebra.
8. The application of advanced algebra knowledge in related courses.
9. Application of Mathematical Software in Advanced Algebra Learning
10. Mathematical modeling case using advanced algebra knowledge
1 1. Application of Higher Algebra Theory in Finance
12. the application of counterexample in higher algebra
13. Research on the application of determinant theory
Application of some special determinants
15. Summary of determinant calculation methods
16. Some applications of Vandermonde determinant
17. Application of linear equation;
18. Generalization of linear equations-from vector to matrix
19. On the Maximum Independent Group of Vector Groups
20. The discriminant method of linear correlation and linear independence of vector groups.
2 1. A summary of solving linear equations
22. Direct method and iterative method for solving linear equations
23. The application of vector
24. The properties of matrix polynomial and its application
25. Some discriminant methods of matrix reversibility
26. Discussion on matrix rank inequality (application)
27. On adjoint matrices of matrices
28. The application of matrix operation in economy
29. On the block matrix
30. Elementary transformation of block matrix and its application
Elementary transformation of 3 1. matrix and its application
32. Geometric characteristics of matrix transformation
33. Positive definite quadratic form and its application
34. Simplification and application of quadratic form
35. The method of transforming quadratic form into standard form
36. The application of matrix diagonalization
37. The concept of matrix canonical form and its application
38. Invariants of matrices under different transformations and their applications
39. The application of linear transformation
40. Application of eigenvalues and eigenvectors
4 1. Some Problems about Linear Transformation
42. Some Questions about Euclidean Space
43. Matrix Equivalence, Contract, Similar Correlation and Its Application
44. The problem of mutual transformation between linear transformation proposition and matrix proposition
45. Linear space and Euclidean space
46. The application of elementary line transformation in vector space Pn
Hamilton-Kelly theorem and its application
48. The geometric significance and application of Schmidt orthogonalization method.
49. The relationship between invariant subspace and Jordan canonical form.
50. Discriminating method of irreducibility of polynomials and its application
Matrix properties and applications of 5 1. quadratic form
52. Block matrix and its application
53. Orthogonal transformation in Euclidean space and its geometric application
54. The properties of symmetric matrix and its application
55. The method of finding the dimension and basis of the intersection of two subspaces.
56. On the Orthogonal Complement of N-dimensional Euclidean Space Subspace
57. Several methods to find Jordan canonical form.
58. Some applications of similarity matrix
59. Several methods to judge the similarity of matrices
60. Some properties of orthogonal matrices
Several equivalent conditions for positive definiteness of 6 1. real symmetric matrix
62. Discussion on Orthogonal Problems in Euclidean Space
63. Matrix eigenvalue and its application in solving problems.
64. The application of eigenvalues and eigenvectors of matrices
65. Simple application of determinant in algebra and geometry
66. The application of inner product inequality in Euclidean space
67. Research on several methods of finding standard orthogonal bases.
68. The application of advanced algebraic theory in economics.
69. The least square method in the matrix
70. Solutions of common linear and Euclidean space bases and standard orthogonal bases.