Linear algebra / W. H. Greub.
Idioma: Inglés Lenguaje original: Alemán Series Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete: Bd. 97.Editor: New York : Springer-Verlag, 1967Edición: 3rd edDescripción: xii, 434 p. ; 24 cmTítulos uniformes: Lineare Algebra. Inglés Tema(s): Algebras, LinearOtra clasificación: 15-01Chapter 0. Prerequisites [1] Chapter I. Vector spaces [5] § 1. Vector spaces [5] §2. Linear mappings [16] § 3. Subspaces and factor spaces [22] § 4. Dimension [32] § 5. The topology of a real finite dimensional vector space [37] Chapter II. Linear mappings [41] § 1. Basic properties [41] § 2. Operations with linear mappings [51] § 3. Linear isomorphisms [54] § 4. Direct sum of vector spaces [55] § 5. Dual vector spaces [62] § 6. Finite dimensional vector spaces [75] Chapter III. Matrices [82] § 1. Matrices and systems of linear equations [82] § 2. Multiplication of matrices [88] § 3. Basis transformation [91] § 4. Elementary transformations [94] Chapter IV. Determinants [98] $ 1. Determinant functions [98] § 2. The determinant of a linear transformation [101] § 3. The determinant of a matrix [105] § 4. Dual determinant functions [108] §5. Cofactors [110] § 6. The characteristic polynomial [116] §7. The trace [122] § 8. Oriented vector spaces [127] Chapter V. Algebras [139] § 1. Basic properties [139] §2. Ideals [153] 6 3. Change of coefficient field of a vector space 15g Chapter VI. Gradations and homology [162] § 1. G-graded vector spaces [162] 82. G-graded algebras [169] § 3. Differential spaces and differential algebras [173] Chapter VII. Inner product spaces [181] 81. The inner product [181] 8 2. Orthonormal bases [186] § 3. Normed determinant functions [190] § 4. Duality in an inner product space [198] § 5. Normed vector spaces [200] Chapter VIII. Linear mappings of inner product spaces [204] §1. The adjoint mapping [204] § 2. Selfadjoint mappings [209] §3. Orthogonal projections [214] §4. Skew mappings [217] § 5. Isometric mappings [220] § 6. Rotations of the plane and of 3-space [225] § 7. Differentiable families of linear automorphisms [232] Chapter IX. Symmetric bilinear functions [244] § 1. Bilinear and quadratic functions [244] § 2. The decomposition of E [248] § 3. Pairs of symmetric bilinear functions [255] § 4. Pseudo-Euclidean spaces [264] § 5. Linear mappings of Pseudo-Euclidean spaces [271] Chapter X. Quadrics [279] § 1. Affine spaces [279] § 2. Quadrics in the affine space [284] § 3. Affine equivalence of quadrics [293] § 4. Quadrics in the Euclidean space [299] Chapter XI. Unitary spaces [308] §1. Hermitian functions [308] § 2. Unitary spaces [310] § 3. Linear mappings of unitary spaces [314] § 4. Unitary mappings of the complex plane [320] § 5. Application to the orthogonal group [324] § 6. Application to Lorentz-transformations [331] Chapter XII. Polynomial algebra [338] § 1. Basic properties [338] § 2. Ideals and divisibility [344] § 3. Products of relatively prime polynomials [353] § 4. Factor algebras [357] § 5. The structure of factor algebras [360] Chapter XIII. Theory of a linear transformation [368] § 1. Polynomials in a linear transformation [368] § 2. Generalized eigenspaces [375] § 3. Cyclic spaces and irreducible spaces [382] § 4. Application of cyclic spaces [397] § 5. Nilpotent and semisimple transformations [406] § 6. Applications to inner product spaces [419] Bibliography [428] Subject Index [430]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 15 G836-3 (Browse shelf) | Available | A-2497 |
Bibliografía: p. [428]-429.
Chapter 0. Prerequisites [1] --
Chapter I. Vector spaces [5] --
§ 1. Vector spaces [5] --
§2. Linear mappings [16] --
§ 3. Subspaces and factor spaces [22] --
§ 4. Dimension [32] --
§ 5. The topology of a real finite dimensional vector space [37] --
Chapter II. Linear mappings [41] --
§ 1. Basic properties [41] --
§ 2. Operations with linear mappings [51] --
§ 3. Linear isomorphisms [54] --
§ 4. Direct sum of vector spaces [55] --
§ 5. Dual vector spaces [62] --
§ 6. Finite dimensional vector spaces [75] --
Chapter III. Matrices [82] --
§ 1. Matrices and systems of linear equations [82] --
§ 2. Multiplication of matrices [88] --
§ 3. Basis transformation [91] --
§ 4. Elementary transformations [94] --
Chapter IV. Determinants [98] --
$ 1. Determinant functions [98] --
§ 2. The determinant of a linear transformation [101] --
§ 3. The determinant of a matrix [105] --
§ 4. Dual determinant functions [108] --
§5. Cofactors [110] --
§ 6. The characteristic polynomial [116] --
§7. The trace [122] --
§ 8. Oriented vector spaces [127] --
Chapter V. Algebras [139] --
§ 1. Basic properties [139] --
§2. Ideals [153] --
6 3. Change of coefficient field of a vector space 15g --
Chapter VI. Gradations and homology [162] --
§ 1. G-graded vector spaces [162] --
82. G-graded algebras [169] --
§ 3. Differential spaces and differential algebras [173] --
Chapter VII. Inner product spaces [181] --
81. The inner product [181] --
8 2. Orthonormal bases [186] --
§ 3. Normed determinant functions [190] --
§ 4. Duality in an inner product space [198] --
§ 5. Normed vector spaces [200] --
Chapter VIII. Linear mappings of inner product spaces [204] --
§1. The adjoint mapping [204] --
§ 2. Selfadjoint mappings [209] --
§3. Orthogonal projections [214] --
§4. Skew mappings [217] --
§ 5. Isometric mappings [220] --
§ 6. Rotations of the plane and of 3-space [225] --
§ 7. Differentiable families of linear automorphisms [232] --
Chapter IX. Symmetric bilinear functions [244] --
§ 1. Bilinear and quadratic functions [244] --
§ 2. The decomposition of E [248] --
§ 3. Pairs of symmetric bilinear functions [255] --
§ 4. Pseudo-Euclidean spaces [264] --
§ 5. Linear mappings of Pseudo-Euclidean spaces [271] --
Chapter X. Quadrics [279] --
§ 1. Affine spaces [279] --
§ 2. Quadrics in the affine space [284] --
§ 3. Affine equivalence of quadrics [293] --
§ 4. Quadrics in the Euclidean space [299] --
Chapter XI. Unitary spaces [308] --
§1. Hermitian functions [308] --
§ 2. Unitary spaces [310] --
§ 3. Linear mappings of unitary spaces [314] --
§ 4. Unitary mappings of the complex plane [320] --
§ 5. Application to the orthogonal group [324] --
§ 6. Application to Lorentz-transformations [331] --
Chapter XII. Polynomial algebra [338] --
§ 1. Basic properties [338] --
§ 2. Ideals and divisibility [344] --
§ 3. Products of relatively prime polynomials [353] --
§ 4. Factor algebras [357] --
§ 5. The structure of factor algebras [360] --
Chapter XIII. Theory of a linear transformation [368] --
§ 1. Polynomials in a linear transformation [368] --
§ 2. Generalized eigenspaces [375] --
§ 3. Cyclic spaces and irreducible spaces [382] --
§ 4. Application of cyclic spaces [397] --
§ 5. Nilpotent and semisimple transformations [406] --
§ 6. Applications to inner product spaces [419] --
Bibliography [428] --
Subject Index [430] --
MR, 37 #221
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