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RELATIVE PERTURBATION BOUNDS FOR THE JOINT SPECTRUM OF COMMUTING TUPLES OF MATRICES

Part of: Basic linear algebra

Published online by Cambridge University Press:  05 July 2018

ARNAB PATRA Open the ORCID record for ARNAB PATRA [Opens in a new window]  and
P. D. SRIVASTAVA Open the ORCID record for P. D. SRIVASTAVA [Opens in a new window]
ARNAB PATRA*
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India email arnptr91@gmail.com
P. D. SRIVASTAVA
Affiliation:
Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India email pds@maths.iitkgp.ernet.in
*
✉arnptr91@gmail.com
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Abstract

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In this paper, we study the relative perturbation bounds for joint eigenvalues of commuting tuples of normal $n\times n$ matrices. Some Hoffman–Wielandt-type relative perturbation bounds are proved using the Clifford algebra technique. We also extend a result for diagonalisable matrices which improves a relative perturbation bound for single matrices.

Keywords

joint eigenvaluesClifford algebracommuting tuple of matrices

MSC classification

Primary: 15A42: Inequalities involving eigenvalues and eigenvectors
Secondary: 15A18: Eigenvalues, singular values, and eigenvectors
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 3 , December 2018 , pp. 414 - 421
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

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