Eigenvalues of matrices with several prescribed blocks. II (Q1870064)

[For part I see ibid. 311, 13-24 (2000; Zbl 0954.15006).] An \(n\times n\) matrix \(C\) with entries from an arbitrary field \(F\) is partitioned into \(k\times k\) blocks \(C_{ij}\) where the diagonal blocks \(C_{11}, \dots, C_{kk}\) are square. The paper investigates the eigenvalues of \(C\) when one \(C_{ii}\) is fixed and the others vary. The main theorem gives necessary and sufficient conditions for the existence of a matrix \(C\) with \(n\) given eigenvalues. Examples are not given, but the paper lists (and uses) related results by the authors and others published during the second half of the twentieth century.