《The Theory of Matrices》求取 ⇩

Ⅰ．Matrices,Arrays and Determinants1

1．Linear algebra1

2．Representation by ordered sets1

3．Total matric algebra2

4．Diagonal and scalar matrices5

5．Transpose．Symmetric and skew matrices5

6．Determinants6

7．Properties of determinants8

8．Rank and nullity10

9．Identities among minors12

10．Reducibility14

11．Arrays and determinants of higher dimension15

12．Matrices in non-commutative systems16

Ⅱ．The characteristic equation17

13．The minimum equation17

14．The characteristic equation17

15．Determination of the minimum equation20

16．Characteristic roots22

17．Conjugate sets24

18．Limits for the characteristic roots25

19．Characteristic roots of unitary matrices28

Ⅲ．Associated Integral Matrices29

20．Matrices with elements in a principal ideal ring29

21．Construction of unimodular matrices31

22．Associated matrices31

23．Greatest common divisors35

24．Linear form moduls37

25．Ideals38

Ⅳ．Equivalence40

26．Equivalent matrices40

27．Invariant factors and elementary divisors43

28．Factorization of a matrix44

29．Polynomial domains45

30．Equivalent pairs of matrices48

31．Automorphic transformations50

Ⅴ．Congruence51

32．Matrices with elements in a principal ideal ring51

33．Matrices with rational integral elements54

34．Matrices with elements in a field56

35．Matrices in an algebraically closed field60

36．Hermitian matrices62

37．Automorphs65

Ⅵ．Similarity68

38．Similar matrices68

39．Matrices with elements in a field69

40．WEYR＇S characteristic73

41．Unitary and orthogonal equivalence75

42．The structure of unitary and orthogonal matrices78

Ⅶ．Composition of matrices81

43．Direct sum and direct product81

44．Product-matrices and power-matrices85

45．Adjugates86

Ⅷ．Matric equations89

46．The general linear equation89

47．Scalar equations94

48．The unilateral equation95

Ⅸ．Functions of Matrices97

49．Power series in matrices97

50．Functions of matrices99

51．Matrices whose elements are functions of complex variables101

52．Derivatives and integrals of matrices102

Ⅹ．Matrices of infinite order104

53．Infinite determinants104

54．Infinite matrices106

55．A matric algebra of infinite order106

56．Bounded matrices108

57．Matrices with a non-denumerable number of rows and colums110