Ⅰ．Matrices,Arrays and Determinants 1
1．Linear algebra 1
2．Representation by ordered sets 1
3．Total matric algebra 2
4．Diagonal and scalar matrices 5
5．Transpose．Symmetric and skew matrices 5
6．Determinants 6
7．Properties of determinants 8
8．Rank and nullity 10
9．Identities among minors 12
10．Reducibility 14
11．Arrays and determinants of higher dimension 15
12．Matrices in non-commutative systems 16
Ⅱ．The characteristic equation 17
13．The minimum equation 17
14．The characteristic equation 17
15．Determination of the minimum equation 20
16．Characteristic roots 22
17．Conjugate sets 24
18．Limits for the characteristic roots 25
19．Characteristic roots of unitary matrices 28
Ⅲ．Associated Integral Matrices 29
20．Matrices with elements in a principal ideal ring 29
21．Construction of unimodular matrices 31
22．Associated matrices 31
23．Greatest common divisors 35
24．Linear form moduls 37
25．Ideals 38
Ⅳ．Equivalence 40
26．Equivalent matrices 40
27．Invariant factors and elementary divisors 43
28．Factorization of a matrix 44
29．Polynomial domains 45
30．Equivalent pairs of matrices 48
31．Automorphic transformations 50
Ⅴ．Congruence 51
32．Matrices with elements in a principal ideal ring 51
33．Matrices with rational integral elements 54
34．Matrices with elements in a field 56
35．Matrices in an algebraically closed field 60
36．Hermitian matrices 62
37．Automorphs 65
Ⅵ．Similarity 68
38．Similar matrices 68
39．Matrices with elements in a field 69
40．WEYR＇S characteristic 73
41．Unitary and orthogonal equivalence 75
42．The structure of unitary and orthogonal matrices 78
Ⅶ．Composition of matrices 81
43．Direct sum and direct product 81
44．Product-matrices and power-matrices 85
45．Adjugates 86
Ⅷ．Matric equations 89
46．The general linear equation 89
47．Scalar equations 94
48．The unilateral equation 95
Ⅸ．Functions of Matrices 97
49．Power series in matrices 97
50．Functions of matrices 99
51．Matrices whose elements are functions of complex variables 101
52．Derivatives and integrals of matrices 102
Ⅹ．Matrices of infinite order 104
53．Infinite determinants 104
54．Infinite matrices 106
55．A matric algebra of infinite order 106
56．Bounded matrices 108
57．Matrices with a non-denumerable number of rows and colums 110