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LINEAR ALGEBRA SECOND EDITIONPDF|Epub|txt|kindle电子书版本下载
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- 出版社： Springer-Verlag
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- 出版时间：未知
- 标注页数：338页
- 文件大小：10MB
- 文件页数：345页
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图书目录
Chapter Ⅰ．Linear spaces1
1．The axioms of a linear space1
2．Linear subspaces7
3．Linear spaces of finite dimension10
Chapter Ⅱ．Linear transformations16
1．Linear mappings16
2．Dual spaces20
3．Dual mappings24
4．Sum and product of linear mappings26
Chapter Ⅲ．Matrices31
1．Matrices and systems of linear equations31
2．Multiplication of matrices37
3．Basis-transformation40
4．Elementary transformations43
Chapter Ⅳ．Determinants46
1．Determinant-functions46
2．The determinant of an endomorphism50
3．The determinant of a matrix53
4．Cofactors57
5．The characteristic polynomial62
6．The trace67
Chapter Ⅴ．Oriented linear spaces71
1．Orientation by a determinant-function71
2．The topology of a linear space74
Chapter Ⅵ．Multilinear mappings81
1．Basic properties81
2．Tensor-product85
Chapter Ⅶ．Tensor-algebra96
1．Tensors96
2．Contraction104
3．The duality of Tpq(E) and Tqp(E)108
Chapter Ⅷ．Exterior algebra112
1．Covariant skew-symmetric tensors112
2．Decomposable skew-symmetric tensors121
3．Mixed skew-symmetric tensors125
4．The duality of Spq(E) and Sqp(E)128
Chapter Ⅸ．Duality in exterior algebra133
1．The dual product133
2．The tensors Jp137
3．The dual isomorphisms142
4．The adjoint tensor148
5．The exterior product157
Chapter Ⅹ．Inner product spaces160
1．The inner product160
2．Orthonormal bases164
3．Normed determinant-functions168
4．The duality in an inner product space175
5．Normed linear spaces182
Chapter Ⅺ．Linear mappings of inner product spaces186
1．The adjoint mapping186
2．Selfadjoint mappings189
3．Orthogonal projections193
4．Skew mappings196
5．Isometric mappings201
6．Rotations of the plane and 3-space205
7．Differentiable families of automorphisms210
Chapter Ⅻ．Symmetric bilinear functions220
1．Bilinear and quadratic functions221
2．The decomposition of E224
3．Simultaneous diagonalization of two bilinear forms231
4．Pseudo-Euclidean spaces237
5．Linear mappings of pseudo-Euclidean spaces244
Chapter ⅩⅢ．Quadrics250
1．Affine spaces250
2．Quadrics in the affine space255
3．Affine equivalence of quadrics263
4．Quadrics in the Euclidean space268
Chapter ⅩⅣ．Unitary spaces275
1．Hermitian functions275
2．Unitary spaces277
3．Linear mappings of a unitary space281
4．Unitary mappings of the complex plane286
5．Applications to the orthogonal group291
6．Application to Lorentz-transformations297
Chapter ⅩⅤ．Invariant subspaces302
1．The algebra of polynomials303
2．Polynomials of endomorphisms307
3．Invariant subspaces313
4．The decomposition of a complex linear space317
5．The decomposition of a real linear space321
6．Application to inner product spaces326
Bibliography333
Subject Index335