A completion problem over the field of real numbers Original Research Article

Let F be a field. Almost 25 years ago, G.N. de Oliveira has proposed the following completion problems: Describe the possible characteristic polynomials of [Ai,j], i,jset membership, variant{1,2}, where A1,1 and A2,2 are square submatrices, when some of the blocks Ai,j are fixed and the others vary [cf. Linear Multilinear Algebra 2 (1975) 357]. Several of these problems remain unsolved. This paper gives the solution, over the field of real numbers, of Oliveiraʹs problem where the blocks A1,2,A2,1 are fixed and the others vary.