Abstract
An n-by-n matrix is called aP-matrix if it is one of (weakly) sign-symmetric, positive, nonnegative P-matrix, (weakly) sign-symmetric, positive, nonnegative P0;1-matrix, or Fischer, or Koteljanskii matrix. In this paper, we are interested in P-matrix completion problems, that is, when a partial P-matrix has a P-matrix completion. Here, we prove that a combinatorially symmetric partial positive P-matrix has a positive P-matrix completion if the graph of its specified entries is an n-cycle. In general, a combinatorially symmetric partial P-matrix has a P-matrix completion if the graph of its specified entries is a 1-chordal graph. This condition is also necessary for (weakly) sign-symmetric P0- or P0;1-matrices. © 2000 Elsevier Science Inc. All rights reserved.
Keywords
P-matrix Matrix completion Graph Combinational symmetry
Referencia
S.M. Fallat, C.R. Johnson, J.R. Torregrosa, A.M. Urbano (2000): P-matrix completions under weak symmetry assumptions. Linear Algebra and its Applications 312 (2000) 73–91.
