Derivatives and perturbation bounds for symmetric tensor powers of matrices

Details Derivatives and perturbation bounds for symmetric tensor powers of matrices Derivatives and perturbation bounds for symmetric tensor powers of matrices

2011-02-11

arxiv.org/abs/1102.2414v2

Mathematics

Functional Analysis

13 pages

Scientific paper

Expressions for all order derivatives for the permanent of a matrix and its
symmetric tensor powers are given. Norms of the derivatives of symmetric tensor
powers are evaluated exactly. From there, an upper bound for the norm of the
derivatives of the permanent is obtained. These are then used to give
perturbation bounds for both these functions.

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