Full-column rank solutions of the matrix equation \(AV\)=\(EVJ\)
Necessary and sufficient conditions are derived for the existence of a full-column rank solution \(V\in\mathbb{C}^{n\times m}\) of the linear matrix equation \(AV= EV J\), where \(A,E\in\mathbb{C}^{n\times n}\) and \(J\in\mathbb{C}^{m\times m}\) are given matrices such that the matrix pencil \(\lambda E- A\) is regular. Such equations arise in the theory of descriptor linear systems \(Ex'= Ax+ Bu\).
scientific article; zbMATH DE number 2082093