BS Physics Notes Series

1. 810
Example
Let

2. 811

3. 812
Diagonalizable Matrix
Orthogonal Matrix
Symmetric Matrix
Unitary Matrix
Example
Let

4. 813
Example
Evaluate the determinant
Solution

5. 814
Example
Example
Solution

6. 815
Example
Solution

7. 816
Theorem
Example

8. 817
Example

9. 818

10. 819
Example

11. 820
Solution
The three determinants required by Cramer’s are
Example
Solution

12. 821
Example
Expand
Solution
Example
Use Cramer’s rule to solve
Solution

13. 822
The determinants involved are
Nonsingular and singular matrices
Norm of a vector
Orthogonal matrices

14. 823
Example
Show that the matrix
is orthogonal.
Solution
We have
Hermitian, skew-Hermitian, and unitary matrices

15. 824
Example
The following are examples of Hermitian, skew-Hermitian, and unitary matrices.

16. 825

17. 826
Mathematical Methods in Physics
209 PDE

18. 827

19. 828

20. 829

21. 830

22. 831

23. 832

24. 833

25. 834

26. 835

27. 836

28. 837

29. 838

30. 839

31. 840

32. 841

33. 842

34. 843

35. 844

36. 845

37. 846

38. 847

39. 848

40. 849

41. 850

42. 851

43. 852

44. 853

45. 854

46. 855

47. 856

48. 857

49. 858

50. 859

51. 860

52. 861

53. 862

54. 863

55. 864

56. 865

57. 866

58. 867

59. 868

60. 869

61. 870

62. 871

63. 872

64. 873

65. 874

66. 875

67. 876

68. 877

69. 878

70. 879

71. 880

72. 881

73. 882

74. 883

75. 884

76. 885

77. 886

78. 887

79. 888

80. 889

81. 890

82. 891

83. 892

84. 893

85. 894

86. 895

87. 896

88. 897

89. 898

90. 899

91. 900

92. 901

93. 902

94. 903

95. 904

96. 905

97. 906

98. 907

99. 908

100. 909