Variation of induced linear operators

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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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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