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The solution of the matrix equations AXB−CXD=E AND (YA−DZ,YC−BZ)=(E,F)

✍ Scribed by King-wah Eric Chu

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
661 KB
Volume
93
Category
Article
ISSN
0024-3795

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✦ Synopsis

The conditions for the existence of a unique solution of the matrix equation AXB -CXD = E are proved to be that (i) the pencils A -XC and D -XB are regular, and (ii) the spectra of the pencils have an empty intersection. A numerical algorithm for solving the equation is proposed. The possibility of a least-squares-type solution is briefly discussed. The set of equations (YA -DZ, YC -BZ) = (E, F) is proved to be equivalent to the aforementioned equation, and its solution is also investigated. A numerical algorithm is proposed.

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