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The complete solution to the Sylvester-polynomial-conjugate matrix equations

โœ Scribed by Ai-Guo Wu; Gang Feng; Wanquan Liu; Guang-Ren Duan

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
253 KB
Volume
53
Category
Article
ISSN
0895-7177

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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

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An explicit solution to the generalized Sylvester matrix equation AX -EXF = BY , with the matrix F being a companion matrix, is given. This solution is represented in terms of the R-controllability matrix of (E, A, B), generalized symmetric operator and a Hankel matrix. Moreover, several equivalent