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Ranks of least squares solutions of the matrix equation

✍ Scribed by Yong Hui Liu

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 224 KB
Volume: 55
Category: Article
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2007.06.023

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✦ Synopsis

For a complex matrix equation AX B = C, we solve the following two problems: (1) the maximal and minimal ranks of least square solution X to AX B = C, and (2) the maximal and minimal ranks of two real matrices X 0 and X 1 in least square solution X = X 0 + iX 1 to AX B = C. We also give a necessary and sufficient condition for matrix equations A i X i B i = C i (i = 1, 2) to have a common least square solution.

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