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THE GENERALIZED SYLVESTER MATRIX EQUATION, RANK MINIMIZATION AND ROTH’S EQUIVALENCE THEOREM

Part of: Basic linear algebra

Published online by Cambridge University Press:  21 July 2011

MINGHUA LIN  and
HARALD K. WIMMER
MINGHUA LIN
Affiliation:
Department of Mathematics, University of Regina, Regina S4S 0A2, Canada (email: lin243@uregina.ca)
HARALD K. WIMMER*
Affiliation:
Mathematisches Institut, Universität Würzburg, 97074 Würzburg, Germany (email: wimmer@mathematik.uni-wuerzburg.de)
*
✉For correspondence; e-mail: wimmer@mathematik.uni-wuerzburg.de
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Abstract

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Roth’s theorem on the consistency of the generalized Sylvester equation AX−YB=C is a special case of a rank minimization theorem.

Keywords

Sylvester’s matrix equationRoth’s equivalence theoremrank minimizationRoth’s similarity theorem

MSC classification

Secondary: 15A24: Matrix equations and identities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 3 , December 2011 , pp. 441 - 443
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

[1]Roth, R. E., ‘The equations AX−Y B=C and AX−XB=C in matrices’, Proc. Amer. Math. Soc. 3 (1952), 392–396.Google Scholar
[2]Tian, Y., ‘The minimal rank of the matrix expression A−BX−Y C’, Missouri J. Math. Sci. 14 (2002), 40–48.CrossRefGoogle Scholar