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Tensor logarithmic norm and its applications
Author(s) -
Ding Weiyang,
Hou Zongyuan,
Wei Yimin
Publication year - 2016
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2064
Subject(s) - logarithm , mathematics , tensor (intrinsic definition) , eigenvalues and eigenvectors , hurwitz matrix , matrix norm , norm (philosophy) , pure mathematics , matrix (chemical analysis) , mathematical analysis , algebra over a field , physics , parametric statistics , statistics , materials science , quantum mechanics , political science , law , composite material
Summary Matrix logarithmic norm is an important quantity, which characterize the stability of linear dynamical systems. We propose the logarithmic norms for tensors and tensor pairs, and extend some classical results from the matrix case. Moreover, the explicit forms of several tensor logarithmic norms and semi‐norms are also derived. Employing the tensor logarithmic norms, we bound the real parts of all the eigenvalues of a complex tensor and study the stability of a class of nonlinear dynamical systems. Copyright © 2016 John Wiley & Sons, Ltd.