Linear Algebra
This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1975, 1975
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| Edition: | 4th ed. 1975 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- § 3. Change of coefficient field of a vector space
- VI. Gradations and homology
- § 1. G-graded vector spaces
- § 2. G-graded algebras
- § 3. Differential spaces and differential algebras
- VII. Inner product spaces
- § 1. The inner product
- § 2. Orthonormal bases
- § 3. Normed determinant functions
- § 4. Duality in an inner product space
- § 5. Normed vector spaces
- § 6. The algebra of quaternions
- VIII. Linear mappings of inner product spaces
- § 1. The adjoint mapping
- § 2. Selfadjoint mappings
- § 3. Orthogonal projections
- § 4. Skew mappings
- § 5. Isometric mappings
- § 6. Rotations of Euclidean spaces of dimension 2, 3 and 4
- § 7. Differentiate families of linear automorphisms
- IX. Symmetric bilinear functions
- § 1. Bilinear and quadratic functions
- § 2. The decomposition of E
- § 3. Pairs of symmetric bilinear functions
- §4. Pseudo-Euclidean spaces
- § 5. Linear mappings of Pseudo-Euclidean spaces
- X. Quadrics
- 0. Prerequisites
- I. Vector spaces
- § 1. Vector spaces
- § 2. Linear mappings
- § 3. Subspaces and factor spaces
- § 4. Dimension
- § 5. The topology of a real finite dimensional vector space
- II. Linear mappings
- § 1. Basic properties
- § 2. Operations with linear mappings
- § 3. Linear isomorphisms
- § 4. Direct sum of vector spaces
- § 5. Dual vector spaces
- § 6. Finite dimensional vector spaces
- III. Matrices
- § 1. Matrices and systems of linear equations
- § 2. Multiplication of matrices
- § 3. Basis transformation
- § 4. Elementary transformations
- IV. Determinants
- § 1. Determinant functions
- § 2. The determinant of a linear transformation
- § 3. The determinant of a matrix
- § 4. Dual determinant functions
- § 5. The adjoint matrix
- § 6. The characteristic polynomial
- § 7. The trace
- § 8. Oriented vector spaces
- V. Algebras
- § 1. Basic properties
- § 2. Ideals
- § 1. Affine spaces
- § 2. Quadrics in the affine space
- § 3. Affine equivalence of quadrics
- § 4. Quadrics in the Euclidean space
- XI. Unitary spaces
- § 1. Hermitian functions
- § 2. Unitary spaces
- § 3. Linear mappings of unitary spaces
- § 4. Unitary mappings of the complex plane
- § 5. Application to Lorentz-transformations
- XII. Polynomial algebra
- § 1. Basic properties
- § 2. Ideals and divisibility
- § 3. Factor algebras
- § 4. The structure of factor algebras
- XIII. Theory of a linear transformation
- § 1. Polynomials in a linear transformation
- § 2. Generalized eigenspaces
- § 3. Cyclic spaces
- § 4. Irreducible spaces
- § 5. Application of cyclic spaces
- § 6. Nilpotent and semisimple transformations
- § 7. Applications to inner product spaces