Polynomial generalized inverses of polynomial matrices (Q1209784)

The authors give necessary and sufficient conditions for the existence of various types of Moore-Penrose polynomial generalized inverses for a given polynomial matrix \(A\) over \(F[\lambda]\), where \(F\) is an arbitrary field with involution. Here \(X\) is a generalized inverse of type \(\{i,j,\dots,\ell\}\) if \(X\) satisfies equations \((i),\;(j),\dots,(\ell)\) from among the following list of Penrose equations: (1) \(AXA=A\), (2) \(XAX=X\), (3) \((AX)^*=AX\), (4) \((XA)^*=XA\).