Author | Greub, W. H. author |
---|---|
Title | Multilinear Algebra [electronic resource] / by W. H. Greub |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1967 |
Connect to | http://dx.doi.org/10.1007/978-3-662-00795-2 |
Descript | 1 illus. online resource |
I. Tensor product -- ยง 1. Multilinear mappings -- ยง 2. Tensor product -- ยง 3. Subspaces and factor spaces -- ยง 4. Direct decompositions -- ยง 5. Linear mappings -- ยง 6. Tensor product of several vector spaces -- ยง 7. Dual spaces -- ยง 8. Finite dimensional vector spaces -- II. Tensor product of vector spaces with additional structure -- ยง 1. Tensor product of algebras -- ยง 2. Tensor product of G-graded vector spaces -- ยง 3. Tensor product of differential spaces -- ยง 4. Tensor product of differential algebras -- III. Tensor algebra -- ยง 1. Tensors -- ยง 2. Tensors over a pair of dual spaces -- ยง 3. Mixed tensors -- ยง 4. Tensor algebra over an inner product space -- IV. Skew symmetry and symmetry in the tensor algebra -- ยง 1. Skew symmetric tensors -- ยง 2. The factor algebra ?E/N (E) -- ยง 3. Symmetric tensors -- ยง 4. The factor algebra ?E/N (E) -- V. Exterior algebra -- ยง 1. Skew symmetric mappings -- ยง 2. Exterior algebra -- ยง 3. Homomorphisms, derivations and antiderivations -- ยง 4. The operator i (a) -- ยง 5. Exterior algebra over a direct sum -- ยง 6. Ideals in ? E -- ยง 7. Ideals and duality -- VI. Mixed exterior algebra -- ยง 1. The algebra ? (E, E*) -- ยง 2. The Poincarรฉ isomorphism -- ยง 3. Applications to linear transformations -- ยง 4. Decomposable elements in ? E and the lattice of subspaces of E -- VII. Symmetric tensor algebra -- ยง 1. Symmetric tensor algebra -- ยง 2. Polynomial algebra -- VIII. Multilinear functions -- ยง 1. Multilinear functions as tensors -- ยง 2. The algebra of skew symmetric functions -- ยง 3. The algebra of symmetric functions