Derivatives of compound matrix valued functions
| Autor: | Brendan P. W. Ames, Hristo S. Sendov |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Applied Mathematics
010102 general mathematics 010103 numerical & computational mathematics 01 natural sciences Square matrix Algebra Integer matrix Matrix (mathematics) Matrix function Symmetric matrix Nonnegative matrix 0101 mathematics Involutory matrix Centrosymmetric matrix Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 433:1459-1485 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2015.08.029 |
| Popis: | Primary matrix functions and spectral functions are two classes of orthogonally invariant functions on a symmetric matrix argument. Many of their properties have been investigated thoroughly and find numerous applications both theoretical and applied in areas ranging from engineering, image processing, optimization and physics. We propose a family of maps that provide a natural connection and generalization of these two classes of functions. The family of maps also contains the well-known multiplicative and additive compound matrices. We explain when each member of this family is a differentiable function and exhibit a formula for its derivative. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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