On the analyticity of k-isotropic functions. Issue 2 (1st February 2019)

• Record Type: Journal Article
• Authors: Jiang, Tianpei; Mousavi, Mehdi S.; Sendov, Hristo S.
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 2(2019)
• Page Start: 228
• Page End: 247
• Publication Date: 2019-02-01
• Subjects: Primary matrix functions -- spectral functions -- isotropic functions -- k-isotropic functions Loewner operator -- symmetric function -- analyticity -- compound matrix -- multiplicative compound matrix -- additive compound matrix -- tensor product -- anti-symmetric tensor product; Primary: 15A18 -- 47A56 -- 49R50 -- Secondary: 05A05 -- 47A75; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1417967
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: The focus of this work is a family of maps from the space of symmetric matrices, , into the space for any, invariant under the conjugate action of the orthogonal group . This family, called the generated k -isotropic functions, generalizes known types of maps with a similar invariance property, such as the spectral, isotropic, primary matrix functions, multiplicative compound, and additive compound matrices on . We give necessary and sufficient conditions for the analyticity of these maps.