Jose, Shani; Sivakumar, K. C. On inverse-positivity of sub-direct sums of matrices. (English) Zbl 1283.15108 Linear Algebra Appl. 439, No. 6, 1670-1677 (2013). Summary: The authors consider the problem of inverse-positivity of a \(k\)-subdirect sum of matrices. The main results provide a solution to an open problem posed recently. MSC: 15B48 Positive matrices and their generalizations; cones of matrices 15A09 Theory of matrix inversion and generalized inverses Keywords:sub-direct sum; inverse-positivity; \(M\)-matrices PDFBibTeX XMLCite \textit{S. Jose} and \textit{K. C. Sivakumar}, Linear Algebra Appl. 439, No. 6, 1670--1677 (2013; Zbl 1283.15108) Full Text: DOI References: [1] Abad, M. F.; Gassó, M. T.; Torregrosa, J. R., Some results about inverse-positive matrices, Appl. Math. Comput., 218, 130-139 (2011) · Zbl 1234.15012 [2] Berman, A.; Plemmons, R. J., Nonnegative Matrices in the Mathematical Sciences (1994), SIAM: SIAM Philadelphia · Zbl 0815.15016 [3] Bru, R.; Pedroche, F.; Szyld, D. B., Subdirect sums of nonsingualr M-matrices and of their inverses, Electron. J. Linear Algebra, 13, 162-174 (2005) · Zbl 1094.15008 [4] Collatz, L., Functional Analysis and Numerical Mathematics (1966), Academic: Academic New York · Zbl 0221.65088 [5] Carlson, D., What are Schur complements, anyway?, Linear Algebra Appl., 74, 257-275 (1986) · Zbl 0595.15006 [6] Fallat, S. M.; Johnson, C. R., Sub-direct sums and positive classes of matrices, Linear Algebra Appl., 288, 149-173 (1999) · Zbl 0973.15013 [7] Johnson, C. R., Matrix completion problems: a survey, Proc. Sympos. Appl. Math., 40, 171-198 (1990) [8] Toselli, A.; Widlund, O., Domain decomposition methods: algorithms and theory, Series in Computational Mathematics, vol. 34 (2005), Springer: Springer New York · Zbl 1069.65138 [9] Varga, R. S., Matrix Iterative Analysis (1962), Prentice Hall: Prentice Hall Englewood Cliffs, NJ · Zbl 0133.08602 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.