Matrix completion problems of block type (Q5942060)

Block matrices of dimension \(n\times n\) over a field with characteristic zero are considered which are partitioned into \(2\times 2\)-block matrices such that both blocks in the diagonal are square. The authors consider the cases that one or both blocks in the first row of this block matrix are given. It is shown that completion of such a matrix to a matrix with given characteristic polynomial is possible by finite rational computation in \(K\). The resulting algorithms were implemented in MAPLE, experiences with this implementation are discussed.