Linear algebra / Ichiro Satake ; translated by Sebastian Koh, Tadatoshi Akiba, Shin-ichiro Ihara.
Idioma: Inglés Lenguaje original: Japonés Series Pure and applied mathematics ; 29Editor: New York : M. Dekker, c1975Descripción: xi, 375 p. : il. ; 24 cmISBN: 0824715969Títulos uniformes: Senkei dais¯ugaku. Inglés Tema(s): Algebras, LinearOtra clasificación: 15-01Preface to the English Edition v Preface to the First Edition vii Instructions to the Reader ix List of Symbols xi Chapter I. Vector and Matrix Operations [1] §1. Vector operations [1] §2. Matrix operations [5] §3. Matrix operations (the case of square matrices) [12] §4. Linear mappings [19] §5. Real and complex numbers [24] §6. Inner product [35] Appendix. On the exponential function of matrices [40] Chapter II. Determinants [45] §1. Permutations [45] §2. Definition and fundamental properties of determinants [54] §3. Expansion of determinants [64] §4. System of linear equations (Cramer’s rule) [71] §5. Product of determinants [74] §6. Some applications [81] Appendix [1.] Appendix [2.] Appendix [3.] Determinants of special forms [91] Characterizing determinants by their multiplication formulas [96] Differentiation of determinants [98] Chapter III. Vector Spaces [100] Linear independence of vectors [100] §2. Subspaces [107] §3. Orthonormal systems and orthogonal complements [113] §4. The rank of a linear mapping (matrix) [118] §5. Systems of linear equations (general case) [125] §6. The axiomatization of vector spaces [131] §7. Change of basis, orthogonal transformations [137] Appendix 1. Idempotent matrices and projections [145] Appendix 2. Systems of linear differential equations [150] Chapter IV. Normalization of Matrices [154] §1. Eigenvalues and eigenvectors [154] §2. Decomposition into eigenspaces [163] §3. Normalization of symmetric matrices [174] §4. Quadratic forms (hermitian forms) [182] §5. Normal matrices [191] §6. The orthogonal groups [198] Appendix 1. Quadratic forms in general [208] Appendix 2. Lie algebras of orthogonal groups [214] Chapter V. Tensor Algebra [221] §1. Dual spaces [221] §2. Tensor products [231] §3. Symmetric tensors and alternating tensors [243] §4. Tensor algebras and Grassmann algebras [251] §5. Extensions and restrictions of the coefficient field [259] Appendix. Group representations [269] Supplement. Geometric Interpretation [292] §1. Vectors in a 3-dimensional space [292] $2. Vector expressions for lines and planes [298] §3. Areas, volumes [393] 54. Axioms of Euclidean geometry [312] §5. Principal axes of quadrics [319] Appendix. The concept of a projective space [325] Answers [329]
Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
---|---|---|---|---|---|---|---|---|
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 15 Sa253 (Browse shelf) | Available | A-4951 |
Traducción de: Senkei dais¯ugaku, cuya 1ª ed. fue publicada en 1958 bajo el título: Gy¯oretsu to gy¯oretsushiki.
"There is little doubt that this is one of the best texts on linear algebra available. It covers material which is interesting, important and central in mathematics and in such applications as numerical linear algebra, control theory and group representation theory. Although many difficult topics are covered, they are done with clarity and incisiveness. I can recommend this book with no reservations. It is a gem."--Marvin Marcus, Math. Rev.
Bibliografía: p. 368-369.
Preface to the English Edition v --
Preface to the First Edition vii --
Instructions to the Reader ix --
List of Symbols xi --
Chapter I. Vector and Matrix Operations [1] --
§1. Vector operations [1] --
§2. Matrix operations [5] --
§3. Matrix operations (the case of square matrices) [12] --
§4. Linear mappings [19] --
§5. Real and complex numbers [24] --
§6. Inner product [35] --
Appendix. On the exponential function of matrices [40] --
Chapter II. Determinants [45] --
§1. Permutations [45] --
§2. Definition and fundamental properties of determinants [54] --
§3. Expansion of determinants [64] --
§4. System of linear equations (Cramer’s rule) [71] --
§5. Product of determinants [74] --
§6. Some applications [81] --
Appendix [1.] --
Appendix [2.] --
Appendix [3.] --
Determinants of special forms [91] --
Characterizing determinants by their multiplication formulas [96] --
Differentiation of determinants [98] --
Chapter III. Vector Spaces [100] --
Linear independence of vectors [100] --
§2. Subspaces [107] --
§3. Orthonormal systems and orthogonal complements [113] --
§4. The rank of a linear mapping (matrix) [118] --
§5. Systems of linear equations (general case) [125] --
§6. The axiomatization of vector spaces [131] --
§7. Change of basis, orthogonal transformations [137] --
Appendix 1. Idempotent matrices and projections [145] --
Appendix 2. Systems of linear differential equations [150] --
Chapter IV. Normalization of Matrices [154] --
§1. Eigenvalues and eigenvectors [154] --
§2. Decomposition into eigenspaces [163] --
§3. Normalization of symmetric matrices [174] --
§4. Quadratic forms (hermitian forms) [182] --
§5. Normal matrices [191] --
§6. The orthogonal groups [198] --
Appendix 1. Quadratic forms in general [208] --
Appendix 2. Lie algebras of orthogonal groups [214] --
Chapter V. Tensor Algebra [221] --
§1. Dual spaces [221] --
§2. Tensor products [231] --
§3. Symmetric tensors and alternating tensors [243] --
§4. Tensor algebras and Grassmann algebras [251] --
§5. Extensions and restrictions of the coefficient field [259] --
Appendix. Group representations [269] --
Supplement. Geometric Interpretation [292] --
§1. Vectors in a 3-dimensional space [292] --
$2. Vector expressions for lines and planes [298] --
§3. Areas, volumes [393] --
54. Axioms of Euclidean geometry [312] --
§5. Principal axes of quadrics [319] --
Appendix. The concept of a projective space [325] --
Answers [329] --
MR, 53 #5616
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