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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A symmetry property of the Fréchet derivative
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by Roy Mathias PDF
Proc. Amer. Math. Soc. 120 (1994), 1067-1070 Request permission

Abstract:

Let $A$ and $B$ be $n \times n$ matrices. We show that the matrix representing the linear transformation \[ X \mapsto {(AXB + BXA)^T}\] (which is from the space of $n \times n$ matrices to itself) with respect to the usual basis is symmetric and show a similar symmetry property for the Fréchet derivative of a function $f(X) = \sum \nolimits _{i = 0}^\infty {{a_i}{X^i}}$ defined on the space of $n \times n$ matrices.
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 120 (1994), 1067-1070
  • MSC: Primary 15A04; Secondary 15A24, 15A57, 15A69
  • DOI: https://doi.org/10.1090/S0002-9939-1994-1216819-0
  • MathSciNet review: 1216819