Understanding Matrix Operations and Determinants in Computer Engineering Mathematics

1. CPE 332Computer Engineering Mathematics II Week 2 Chapter 2 Matrix

2. Today Topics • Chapter 2: Matrix • Break • Download Homework 2: Chapter 2 Due Next Week

4. Definition of Matrix

5. Row Matrix, ColumnMatrix

6. Basic Operations

7. Matrix Multiplication

8. Square Matrix

9. Matrix Transpose

10. Types of Matrix

11. Types of Matrix

12. Types of Matrix

13. Types of Matrix

14. Types of Matrix

15. Matrix Inverse

16. Orthogonal/Unitary Matrix

17. Orthogonal Vector

18. Orthogonal Vector

19. Examples

20. Examples

21. Examples

22. Examples

23. Examples

24. Examples

25. Determinant

26. Determinant of Matrix • Given square matrix, determinant of a matrix A written |A| is defined by recursive equation as • Starting from [a1x1] = a, and det(a)=a

27. Sign Matrix • Given matrix A of order nxn • Sign matrix of A is the matrix in the form B=[bij]=[(-1)(i+j)]

28. Minor aij • Is the determinant of matrix A after taken out row ith and jth column.

29. Cofactor aij • Cofactor aij is the minor aij with the sign according to sign pattern • Matrix of cofactor of A is the matrix B which each element bij is the cofactor aij

30. Determinant

31. Calculation of Determinant

32. Calculation of Determinant Complexity = O(n!)

34. คุณสมบัติของ Determinant

35. คุณสมบัติของ Determinant

36. การหา Determinant

38. การหา Determinant

39. Inverse of Matrix

40. Inverse of Matrix

41. Inverse of Matrix

42. Inverse of Matrix

43. Inverse of Matrix

44. Matrix Norms

45. Norms เรียก Spectral Radius ของ X

46. System of Linear Equations

47. System of Linear Equations

48. Reduced Matrix

49. Reduced Matrix

50. Reduced Matrix