Linear algebra / by Werner H. Greub.
Series Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete: Bd. 97.Editor: Berlin : Springer-Verlag, 1963Edición: 2nd edDescripción: x, 338 p. ; 24 cmOtra clasificación: 15-01Contents Chapter I. Linear spaces [1] § 1. The axioms of a linear space [1] § 2. Linear subspaces [7] § 3. Linear spaces of finite dimension [10] Chapter II. Linear transformations [16] § 1. Linear mappings [16] § 2. Dual spaces [20] § 3. Dual mappings [24] § 4. Sum and product of linear mappings [26] Chapter III. Matrices [31] § 1. Matrices and systems of linear equations [31] § 2. Multiplication of matrices [37] § 3. Basis-transformation [40] § 4. Elementary transformations [43] Chapter IV. Determinants [46] § 1. Determinant-functions [46] § 2. The determinant of an endomorphism [50] § 3. The determinant of a matrix [53] § 4. Cofactors [57] § 5. The characteristic polynomial [62] § 6. The trace [67] Chapter V. Oriented linear spaces [71] § 1. Orientation by a determinant-function [71] § 2. The topology of a linear space [74] Chapter VI. Multilinear mappings [81] § 1. Basic properties [81] § 2. Tensor-product [85] Chapter VII. Tensor-algebra [96] § 1. Tensors [96] § 2. Contraction [104] § 3. The duality of Tpq(E) and Tqp (E) [108] Chapter VIII. Exterior algebra [112] § 1. Covariant skew-symmetric tensors [112] § 2. Decomposable skew-symmetric tensors [121] § 3. Mixed skew-symmetric tensors [125] § 4. The duality of Spq(E) and Sqp(E) [128] Chapter IX. Duality in. exterior algebra [133] § 1. The dual product [133] § 2. The tensors Jp [137] §3. The dual isomorphisms [142] § 4. The adjoint tensor [148] § 5. The exterior product [157] Chapter X. Inner product spaces [160] § 1. The inner product [160] § 2. Orthonormal bases [164] § 3. Normed determinant-functions [168] § 4. The duality in an inner product space [175] § 5. Normed linear spaces [182] Chapter XI. Linear mappings of inner product spaces [186] § 1. The adjoint mapping [186] § 2. Selfadjoint mappings [189] § 3. Orthogonal projections [193] § 4. Skew mappings [196] § 5. Isometric mappings [201] § 6. Rotations of the plane and 3-space [205] § 7. Differentiable families of automorphisms [210] Chapter XII. Symmetric bilinear functions [220] § 1. Bilinear and quadratic functions [221] § 2. The decomposition of E [224] § 3. Simultaneous diagonalization of two bilinear forms [231] § 4. Pseudo-Euclidean spaces [237] § 5. Linear mappings of pseudo-Euclidean spaces [244] Chapter XIII. Quadrics [250] § 1. Affine spaces [250] § 2. Quadrics in the affine space [255] § 3. Affine equivalence of quadrics [263] § 4. Quadrics in the Euclidean space [268] Chapter XIV. Unitary spaces [275] § 1. Hermitian functions [275] § 2. Unitary spaces [277] § 3. Linear mappings of a unitary space [281] § 4. Unitary mappings of the complex plane [286] § 5. Applications to the orthogonal group [291] § 6. Application to Lorentz-transformations [297] Chapter XV. Invariant subspaces [302] § 1. The algebra of polynomials [303] § 2. Polynomials of endomorphisms [307] § 3. Invariant subspaces [313] § 4. The decomposition of a complex linear space [317] § 5. The decomposition of a real linear space [321] § 6. Application to inner product spaces [326] Bibliography [333] Subject Index [335]
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Contents --
Chapter I. Linear spaces [1] --
§ 1. The axioms of a linear space [1] --
§ 2. Linear subspaces [7] --
§ 3. Linear spaces of finite dimension [10] --
Chapter II. Linear transformations [16] --
§ 1. Linear mappings [16] --
§ 2. Dual spaces [20] --
§ 3. Dual mappings [24] --
§ 4. Sum and product of linear mappings [26] --
Chapter III. Matrices [31] --
§ 1. Matrices and systems of linear equations [31] --
§ 2. Multiplication of matrices [37] --
§ 3. Basis-transformation [40] --
§ 4. Elementary transformations [43] --
Chapter IV. Determinants [46] --
§ 1. Determinant-functions [46] --
§ 2. The determinant of an endomorphism [50] --
§ 3. The determinant of a matrix [53] --
§ 4. Cofactors [57] --
§ 5. The characteristic polynomial [62] --
§ 6. The trace [67] --
Chapter V. Oriented linear spaces [71] --
§ 1. Orientation by a determinant-function [71] --
§ 2. The topology of a linear space [74] --
Chapter VI. Multilinear mappings [81] --
§ 1. Basic properties [81] --
§ 2. Tensor-product [85] --
Chapter VII. Tensor-algebra [96] --
§ 1. Tensors [96] --
§ 2. Contraction [104] --
§ 3. The duality of Tpq(E) and Tqp (E) [108] --
Chapter VIII. Exterior algebra [112] --
§ 1. Covariant skew-symmetric tensors [112] --
§ 2. Decomposable skew-symmetric tensors [121] --
§ 3. Mixed skew-symmetric tensors [125] --
§ 4. The duality of Spq(E) and Sqp(E) [128] --
Chapter IX. Duality in. exterior algebra [133] --
§ 1. The dual product [133] --
§ 2. The tensors Jp [137] --
§3. The dual isomorphisms [142] --
§ 4. The adjoint tensor [148] --
§ 5. The exterior product [157] --
Chapter X. Inner product spaces [160] --
§ 1. The inner product [160] --
§ 2. Orthonormal bases [164] --
§ 3. Normed determinant-functions [168] --
§ 4. The duality in an inner product space [175] --
§ 5. Normed linear spaces [182] --
Chapter XI. Linear mappings of inner product spaces [186] --
§ 1. The adjoint mapping [186] --
§ 2. Selfadjoint mappings [189] --
§ 3. Orthogonal projections [193] --
§ 4. Skew mappings [196] --
§ 5. Isometric mappings [201] --
§ 6. Rotations of the plane and 3-space [205] --
§ 7. Differentiable families of automorphisms [210] --
Chapter XII. Symmetric bilinear functions [220] --
§ 1. Bilinear and quadratic functions [221] --
§ 2. The decomposition of E [224] --
§ 3. Simultaneous diagonalization of two bilinear forms [231] --
§ 4. Pseudo-Euclidean spaces [237] --
§ 5. Linear mappings of pseudo-Euclidean spaces [244] --
Chapter XIII. Quadrics [250] --
§ 1. Affine spaces [250] --
§ 2. Quadrics in the affine space [255] --
§ 3. Affine equivalence of quadrics [263] --
§ 4. Quadrics in the Euclidean space [268] --
Chapter XIV. Unitary spaces [275] --
§ 1. Hermitian functions [275] --
§ 2. Unitary spaces [277] --
§ 3. Linear mappings of a unitary space [281] --
§ 4. Unitary mappings of the complex plane [286] --
§ 5. Applications to the orthogonal group [291] --
§ 6. Application to Lorentz-transformations [297] --
Chapter XV. Invariant subspaces [302] --
§ 1. The algebra of polynomials [303] --
§ 2. Polynomials of endomorphisms [307] --
§ 3. Invariant subspaces [313] --
§ 4. The decomposition of a complex linear space [317] --
§ 5. The decomposition of a real linear space [321] --
§ 6. Application to inner product spaces [326] --
Bibliography [333] --
Subject Index [335] --
MR, 28 #1201
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