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- W4205437167 abstract "For a real matrix A, Q(A) denotes the set of all matrices with the same sign pattern as A. A linear system Ax=b is signsolvable if solvability and Q(x) depend only on Q(A) and Q(b). The study of signsolvability can be decomposed into the study of L-matrices and of S-matrices, where A is an L-matrix [S-matrix] if the nullspace of each member of Q(A) is {0} [is a line intersecting the open positive orthant]. The problem of recognizing L-matrices is shown to be NP-complete, even in the [almost square] case. Recognition of square L-matrices was transformed into a graph-theoretic problem by Bassett, Maybee, and Quirk in 1968. The complexity of this problem remains open, but that of some related graph-theoretic problems is determined. The relation between S-matrices and L-matrices is studied, and it is shown that a certain recursive construction yields all S-matrices, thus proving a 1964 conjecture of Gorman." @default.
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- W4205437167 date "1984-06-01" @default.
- W4205437167 modified "2023-09-29" @default.
- W4205437167 title "Signsolvability revisited" @default.
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- W4205437167 doi "https://doi.org/10.1016/0024-3795(84)90164-2" @default.
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