On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction

الملخص EN

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 .