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On extremal ranks and least squares solutions subject to a rank restriction. (English) Zbl 1470.65065

Summary: We discuss the feasible interval of the parameter \(k\) and a general expression of matrix \(X\) which satisfies the rank equation \(r(A - B X C) = k\). With these results, we study two problems under the rank constraint \(r(A - B X C) = k\). The first one is to determine the maximal and minimal ranks under the rank constraint \(r(A - B X C) = k\). The second one is to derive the least squares solutions of \(\| B X C - A \|_F = \min\) under the rank constraint \(r(A - B X C) = k\).

MSC:

65F20 Numerical solutions to overdetermined systems, pseudoinverses
15A24 Matrix equations and identities
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References:

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