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Best approximate solutions to matrix equations under rank restrictions

โœ Scribed by Sondermann, Dieter

Book ID
112943513
Publisher
Springer-Verlag
Year
1986
Weight
302 KB
Volume
27
Category
Article
ISSN
0039-0631

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## Abstract We consider the Sylvester equation __AX__โˆ’__XB__+__C__=0 where the matrix __C__โˆˆโ„‚^__n__ร—__m__^ is of low rank and the spectra of __A__โˆˆโ„‚^__n__ร—__n__^ and __B__โˆˆโ„‚^__m__ร—__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for