Derivatives of compound matrix valued functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Ames, Brendan P. W.¹  Sendov, Hristo S.² 

[1] Univ Alabama, Dept Math, Tuscaloosa, AL 35487 USA

[2] Univ Western Ontario, Dept Stat & Actuarial Sci, London, ON N6A 5B7, Canada

关键词: Primary matrix functions;    Spectral functions;    Compound matrix;    Differentiability;    Multiplicative compound matrix;    Additive compound matrix;   

DOI  :  10.1016/j.jmaa.2015.08.029

来源: Elsevier

【 摘 要 】

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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free