Completion problems for real matrices, II

Thirty years ago, G. N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of , where C1,1 and C2,2 are square submatrices, when some of the blocks Ci,j are fixed and the others vary. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveira’s problem where the blocks C1,1,C2,2 are fixed and the others vary.