Derivatives of compound matrix valued functions

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• 作者：Brendan P.W. Ames^a ; ^{bpames@ua.edu" class="auth_mail" title="E-mail the corresponding author} ; Hristo S. Sendov^b ; ^{hssendov@stats.uwo.ca" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Primary matrix functions ; Spectral functions ; Compound matrix ; Differentiability ; Multiplicative compound matrix ; Additive compound matrix
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 January 2016
• 年：2016
• 卷：433
• 期：2
• 页码：1459-1485
• 全文大小：514 K

文摘

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.