Differentiating matrix functions
| Autor: | Kelly Bickel |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
Algebra and Number Theory 010102 general mathematics Derivative Space (mathematics) Notation 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis Mathematics Subject Classification Matrix function 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Tuple Analysis Mathematics |
| Zdroj: | Operators and Matrices. :71-90 |
| ISSN: | 1846-3886 |
| DOI: | 10.7153/oam-07-03 |
| Popis: | 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. 20 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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