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.References
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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