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On inverse-positivity of sub-direct sums of matrices. (English) Zbl 1283.15108

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
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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
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