Bhatia, Rajendra ; Dias da Silva, J. A. (2002) Variation of induced linear operators Linear Algebra and its Applications, 341 (1-3). pp. 391-402. ISSN 0024-3795
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Official URL: http://dx.doi.org//10.1016/S0024-3795(01)00496-7
Related URL: http://dx.doi.org/10.1016/S0024-3795(01)00496-7
Abstract
Let V be an n-dimensional inner product space. Let λ be an irreducible character of the symmetric group Sm, and let Vλ be the symmetry class of tensors associated with it. Let A be a linear operator on V and let Kλ (A) be the operator it induces on Vλ . We obtain an explicit expression for the norm of the derivative of the map A→Kλ (A) in terms of the singular values of A. Two special cases of this problem-antisymmetric and symmetric tensor products-have been studied earlier, and our results reduce to the earlier ones in these cases.
| Item Type: | Article |
|---|---|
| Source: | Copyright of this article belongs to Elsevier Science. |
| Keywords: | Symmetry Class of Tensors; Induced Linear Operator; Derivative; Norm; Positive Linear Operator |
| ID Code: | 2574 |
| Deposited On: | 08 Oct 2010 06:54 |
| Last Modified: | 08 Oct 2010 06:54 |
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