Conditions for a matrix Kronecker lemma (Q1076109)

The author first provides a sufficiency condition for convergence of the sequence \(Q_ n^{-1}\sum^{n}_{k=1}Q_ ka_ k\) with matrices \(Q_ k\) and vectors \(a_ k\). Then necessary conditions for the limit of the sequence to be zero are derived. These conditions contain restrictions on the eigenvalues of \(Q_ n\) and contain as a special case such restrictions as have been obtained by \textit{B. Anderson} and \textit{J. Moore} [ibid. 15, 227-234 (1976; Zbl 0356.15019)].