Linear algebra / George D. Mostow, Joseph H. Sampson.
Series International series in pure and applied mathematicsEditor: New York : McGraw-Hill, c1969Descripción: x, 296 p. : il. ; 24 cmTema(s): Algebras, LinearOtra clasificación: 15-01 (15A69)chapter 1 | vector spaces and inner products [1] 1. Introduction [1] 2. The vector space of 3-tuples [5] 3. The field of complex numbers [7] 4. Real and complex vector spaces [14] 5. The vector spaces Cn and Rn [19] 6. Length and angles in Cn and Rn [21] 7. Subspaces of a vector space [27] 8. Vector spaces of functions [33] 9. Inner-product spaces [41] chapter 2 | linear mappings and linear dependence [48] 1. Introduction [48] Mappings [48] 3. Linear mappings of vector spaces [51] 4. The algebra of linear mappings [58] 5. Linear dependence and dimension [66] 6. Orthonormal bases; unitary and hermitian mappings [76] chapter 3 | matrix algebra [84] 1. Introduction [84] 2. Matrices [84] 3. Matrix coordinates for linear mappings [95] 4. Change of base [105] 5. Rank of a matrix and systems of linear equations [109] 6. Row equivalence, column equivalence, and diagonal form [116] 7. Computation of matrix inverses [130] x chapter 4 | determinants, eigenvalues, eigenvectors [135] 1. Introduction [135] 2. Polynomials [186] 3. Axioms for determinants [139] 4. Computations of determinants and some applications [148] 5. The characteristic polynomial; eigenvalues and eigenvectors [157] 6. Some additional properties of eigenvalues, etc. [164] 7. The Cayley-Hamilton theorem; functions of matrices [171] 8. Determinants as volumes [176] 9. Oriented vector spaces [180] 10. The cross product in three-dimensional spaces, the Frenet formulas [182] 11. Differentiation of determinants [188] chapter 5 | hermitian forms and spectral decomposition [190] 1. Introduction [190] 2. Matrix coordinates of bilinear and antibilinear functions [190] 3. Change of base and Babylonian reduction to diagonal form [198] 4. Hermitian mappings [208] 5. Reformulations of the spectral decomposition theorem [214] 6. Unitary mappings [222] chapter 6 | triangulation of matrices and the Jordan Normal form [224] 1. Introduction [224] 2. Triangular matrices [225] 3. Reduction to triangular form [228] 4. Applications to the hermitian and unitary cases [230] 5. Functions of linear mappings and matrices [231] 6. Characteristic subspaces [233] 7. On the decomposition of linear operators [239] 8. Nilpotent mappings and the Jordan normal form [242] 9. Some comments on the reduction to normal form [246] chapter 7 | multilinear algebra and tensors [247] 1. Introduction [247] 2. Multilinear functions; tensors [248] 3. Dual vector spaces [252] 4. Tensors on a vector space [258] 5. Tensors on a complex space [271] 6. Exterior algebras of real vector spaces [279] index [291]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 15 M916 (Browse shelf) | Available | A-4317 |
chapter 1 | vector spaces and inner products [1] --
1. Introduction [1] --
2. The vector space of 3-tuples [5] --
3. The field of complex numbers [7] --
4. Real and complex vector spaces [14] --
5. The vector spaces Cn and Rn [19] --
6. Length and angles in Cn and Rn [21] --
7. Subspaces of a vector space [27] --
8. Vector spaces of functions [33] --
9. Inner-product spaces [41] --
chapter 2 | linear mappings and linear dependence [48] --
1. Introduction [48] --
Mappings [48] --
3. Linear mappings of vector spaces [51] --
4. The algebra of linear mappings [58] --
5. Linear dependence and dimension [66] --
6. Orthonormal bases; unitary and hermitian mappings [76] --
chapter 3 | matrix algebra [84] --
1. Introduction [84] --
2. Matrices [84] --
3. Matrix coordinates for linear mappings [95] --
4. Change of base [105] --
5. Rank of a matrix and systems of linear equations [109] --
6. Row equivalence, column equivalence, and diagonal form [116] --
7. Computation of matrix inverses [130] --
x chapter 4 | determinants, eigenvalues, eigenvectors [135] --
1. Introduction [135] --
2. Polynomials [186] --
3. Axioms for determinants [139] --
4. Computations of determinants and some applications [148] --
5. The characteristic polynomial; eigenvalues and eigenvectors [157] --
6. Some additional properties of eigenvalues, etc. [164] --
7. The Cayley-Hamilton theorem; functions of matrices [171] --
8. Determinants as volumes [176] --
9. Oriented vector spaces [180] --
10. The cross product in three-dimensional spaces, the Frenet formulas [182] --
11. Differentiation of determinants [188] --
chapter 5 | hermitian forms and spectral decomposition [190] --
1. Introduction [190] --
2. Matrix coordinates of bilinear and antibilinear functions [190] --
3. Change of base and Babylonian reduction to diagonal form [198] --
4. Hermitian mappings [208] --
5. Reformulations of the spectral decomposition theorem [214] --
6. Unitary mappings [222] --
chapter 6 | triangulation of matrices and the Jordan Normal form [224] --
1. Introduction [224] --
2. Triangular matrices [225] --
3. Reduction to triangular form [228] --
4. Applications to the hermitian and unitary cases [230] --
5. Functions of linear mappings and matrices [231] --
6. Characteristic subspaces [233] --
7. On the decomposition of linear operators [239] --
8. Nilpotent mappings and the Jordan normal form [242] --
9. Some comments on the reduction to normal form [246] --
chapter 7 | multilinear algebra and tensors [247] --
1. Introduction [247] --
2. Multilinear functions; tensors [248] --
3. Dual vector spaces [252] --
4. Tensors on a vector space [258] --
5. Tensors on a complex space [271] --
6. Exterior algebras of real vector spaces [279] --
index [291] --
MR, 42 #7673
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