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Find the title of the thesis of advanced algebra course
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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.