Document Zbl 0488.15011

Inverse M-matrices. (English) Zbl 0488.15011

Linear Algebra Appl. 47, 195-216 (1982).

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MSC:

15B48	Positive matrices and their generalizations; cones of matrices
15A45	Miscellaneous inequalities involving matrices
15A23	Factorization of matrices

Keywords:

inverse M-matrices; totally nonnegative matrices; survey; diagonal dominance; diagonal Lyapunov solutions; LU-decompositions; determinantal inequalities; open problems

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References:

[1]	Berman, A.; Plemmons, R., Nonnegative Matrices in the Mathematical Sciences (1979), Academic: Academic New York · Zbl 0484.15016
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[5]	G.M. Engel, personal communication.; G.M. Engel, personal communication.
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[11]	Lewin, M.; Neumann, M., On the inverse \(M\)-matrix problem for (0,1)-matrices, Linear Algebra Appl., 30, 41-50 (1980) · Zbl 0434.05051
[12]	M. Lewin, Totally nonnegative, \(M\); M. Lewin, Totally nonnegative, \(M\) · Zbl 0497.15011
[13]	Markham, T. L., Nonnegative matrices whose inverses are \(M\)-matrices, Proc. Amer. Math. Soc., 36, 326-330 (1972) · Zbl 0281.15016
[14]	Markham, T. L., Two properties of \(M\)-matrices, Linear Algebra Appl., 28, 131-134 (1979) · Zbl 0439.15011
[15]	Neumann, M.; Plemmons, R., Generalized inverse-positivity and splittings of \(M\)-matrices, Linear Algebra Appl., 23, 21-35 (1979) · Zbl 0407.15005
[16]	M. Neumann and R. Plemmons, \(MM\)Linear and Multilinear Algebra; M. Neumann and R. Plemmons, \(MM\)Linear and Multilinear Algebra · Zbl 0455.15006
[17]	Plemmons, R. J., \(M\)-matrix characterizations. I—Nonsingular \(M\)-matrices, Linear Algebra Appl., 18, 175-188 (1977) · Zbl 0359.15005
[18]	M. Stadelmaier, N. Rose, G. Poole, and C. Meyer, Nonnegative matrices with power invariant zero patterns, manuscript.; M. Stadelmaier, N. Rose, G. Poole, and C. Meyer, Nonnegative matrices with power invariant zero patterns, manuscript. · Zbl 0476.15004
[19]	Taussky, O., Research Problem 11, Bull. Amer. Math. Soc., 64, 124 (1958)
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