Author | Greub, W. H. author |
---|---|
Title | Linear Algebra [electronic resource] / by W. H. Greub |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1967 |
Edition | Third Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-00672-6 |
Descript | online resource |
0. Prerequisites -- I. Vector spaces -- ยง 1. Vector spaces -- ยง 2. Linear mappings -- ยง 3. Subspaces and factor spaces -- ยง 4. Dimension -- ยง 5. The topology of a real finite dimensional vector space -- II. Linear mappings -- ยง 1. Basic properties -- ยง 2. Operations with linear mappings -- ยง 3. Linear isomorphisms -- ยง 4. Direct sum of vector spaces -- ยง 5. Dual vector spaces -- ยง 6. Finite dimensional vector spaces -- III. Matrices -- ยง 1. Matrices and systems of linear equations -- ยง 2. Multiplication of matrices -- ยง 3. Basis transformation -- ยง 4. Elementary transformations -- IV. Determinants -- ยง 1. Determinant functions -- ยง 2. The determinant of a linear transformation -- ยง 3. The determinant of a matrix -- ยง 4. Dual determinant functions -- ยง 5. Cofactors -- ยง 6. The characteristic polynomial -- ยง 7. The trace -- ยง 8. Oriented vector spaces -- V. Algebras -- ยง 1. Basic properties -- ยง 2. Ideals -- ยง 3. Change of coefficient field of a vector space -- VI. Gradations and homology -- ยง 1. G-graded vector spaces -- ยง 2. G-graded algebras -- ยง 3. Differential spaces and differential algebras -- VII. Inner product spaces -- ยง 1. The inner product -- ยง 2. Orthonormal bases -- ยง 3. Normed determinant functions -- ยง 4. Duality in an inner product space -- ยง 5. Normed vector spaces -- VIII. Linear mappings of inner product spaces -- ยง 1. The adjoint mapping -- ยง 2. Selfadjoint mappings -- ยง 3. Orthogonal projections -- ยง 4. Skew mappings -- ยง 5. Isometric mappings -- ยง 6. Rotations of the plane and of 3-space -- ยง 7. Differentiable families of linear automorphisms -- IX. Symmetric bilinear functions -- ยง 1. Bilinear and quadratic functions -- ยง 2. The decomposition of E . -- ยง 3. Pairs of symmetric bilinear functions -- ยง 4. Pseudo-Euclidean spaces -- ยง 5. Linear mappings of Pseudo-Euclidean spaces -- X. Quadrics -- ยง 1. Affine spaces -- ยง 2. Quadrics in the affine space -- ยง 3. Affine equivalence of quadrics -- ยง 4. Quadrics in the Euclidean space -- XI. Unitary spaces -- ยง 1. Hermitian functions -- ยง 2. Unitary spaces -- ยง 3. Linear mappings of unitary spaces -- ยง 4. Unitary mappings of the complex plane -- ยง 5. Application to the orthogonal group -- ยง 6. Application to Lorentz-transformations -- XII. Polynomial algebra -- ยง 1. Basic properties -- ยง 2. Ideals and divisibility -- ยง 3. Products of relatively prime polynomials -- ยง 4. Factor algebras -- ยง 5. The structure of factor algebras -- XIII. Theory of a linear transformation -- ยง 1. Polynomials in a linear transformation -- ยง 2. Generalized eigenspaces -- ยง 3. Cyclic spaces and irreducible spaces -- ยง 4. Application of cyclic spaces -- ยง 5. Nilpotent and semisimple transformations -- ยง 6. Applications to inner product spaces