We discuss the feasible interval of the parameter and a general expression of matrix which satisfies the rank equation . With these results, we study two problems under the rank constraint . The first one is to determine the maximal and minimal ranks under the rank constraint . The second one is to derive the least squares solutions of under the rank constraint .
Hongxing Wang. Yeguo Sun. "On Extremal Ranks and Least Squares Solutions Subject to a Rank Restriction." Abstr. Appl. Anal. 2014 (SI10) 1 - 7, 2014. https://doi.org/10.1155/2014/457298