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- W4299493851 abstract "Multivariable, real-valued functions induce matrix-valued functions defined on the space of d-tuples of n-times-n pairwise-commuting self-adjoint matrices. We examine the geometry of this space of matrices and conclude that the best notion of differentiation of these matrix-valued functions is differentiation along curves. We prove that a C^1 real-valued function always induces a C^1 matrix function and give an explicit formula for the derivative. We also show that every real-valued C^m function defined on an open rectangle in the plane induces a matrix-valued function that can be m-times continuously differentiated along C^m curves." @default.
- W4299493851 created "2022-10-02" @default.
- W4299493851 creator A5032393116 @default.
- W4299493851 date "2011-04-02" @default.
- W4299493851 modified "2023-09-26" @default.
- W4299493851 title "Differentiating Matrix Functions" @default.
- W4299493851 doi "https://doi.org/10.48550/arxiv.1104.0336" @default.
- W4299493851 hasPublicationYear "2011" @default.
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