Article ID Journal Published Year Pages File Type
4603390 Linear Algebra and its Applications 2008 14 Pages PDF
Abstract

In this paper, the problem of when the sub-direct sum of two strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix is studied. In particular, it is shown that the subdirect sum of overlapping principal submatrices of strictly diagonally dominant P-matrices is a strictly diagonally dominant P-matrix. It is also established that the 2-subdirect sum of two totally nonnegative matrices is a totally nonnegative matrix under some conditions. It is obtained that a partial totally nonnegative matrix, whose graph of the specified entries is a monotonically labeled 2-chordal graph, has a totally nonnegative completion. Finally, a positive answer to the question (IV) in Fallat and Johnson [Shaun M. Fallat, C.R. Johnson, J.R. Torregrosa, A.M. Urbano, P-matrix completions under weak symmetry assumptions, Linear Algebra Appl. 312 (2000) 73–91] is given for P0-matrices.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory