CHAPTER Ⅰ．LINEAR MANIFOLDS AND LINEAR TRANSFORMATIONS IN Bn 1
1．Vectors and operations on vectors 1
2．Linear manifolds 8
3．Projections;orthonormal bases of a L．M．;complete orthonormal systems 12
4．Products and sums of L．M．＇s 17
5．Orthogonal complements;systems of homogeneous linear equations 21
6．Linear transformations;systems of non-homogeneous linear equations 24
7．Sums and products of L．T．＇s 34
CHAPTER Ⅱ．SPECIAL LINEAR TRANSFORMATIONS IN Bn 40
8．Hermitian transformations;eigen-values，eigen-manifolds and reduction 40
9．Normal transformations and unitary transformations 45
10．Projectors 49
CHAPTER Ⅲ．SPECTRAL REPRESENTATION OF HERMITIAN TRANSFORMATIONS IN Bn 58
11．Continuous functions in Bn 58
12．Orthonormal systems of eigen-solutions of a H．T．The spectral representations 60
13．Unitary transformations of a Hermitian form to principal axes 67
14．Further maximal properties of the eigen-values．inequalities 73
15．Functional calculus of H．T．＇s．The resolvent and its properties 78
16．Transformations commutative with H．T．＇s．Normal transformations 86
CHAPTER Ⅳ．SPECTRAL PROPERTIES OF LINEAR TRANSFORMATIONS IN Bn 97
17．Eigen-values and principal manifolds 97
18．The minimal polynomial 103
19．Functional calculus for L．T．＇s．The resolvent 108
20．Canonical bases of a principal manifold 117
21．Jordan＇s canonical form for a nilpotent L．T．Commutativity 122
22．Jordan＇s canonical form for any L．T．;elementary divisors and Segre characteristic;similar transformations 130
23．Commutativity of L．T．＇s 138
CHAPTER Ⅴ．VECTOR SPACES WITH POSITIVE HERMITIAN METRIC FORMS 151
24．The spaces B＇n and Bn0 151
25．Hermitian forms in B＇n and Bn0 and the pencil H－λG in Bn 159
26．L．T．＇s that are Hermitian or normal in some B＇n 164
27．Application to the dynamical theory of small oscillations 166
Notes 170
References 184
Index of Authors 190
General Index 191