On signed spaces
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We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of e A is S, for each e A ∈ Q(A). In this paper, we show that the number of sign patterns of elements in the row space of S^*-matrix is 3^(m+1) - 2^(m+2) + 2. Also the number of sign patterns of vectors in the null-space of a totally L-matrix is obtained.
Abstract
We denote by Q(A) the set of all matrices with the same sign pattern as A. A matrix A has signed null-space provided there exists a set S of sign patterns such that the set of sign patterns of vectors in the null-space of e A is S, for each e A ∈ Q(A). In this paper, we show that the number of sign patterns of elements in the row space of S^*-matrix is 3^(m+1) - 2^(m+2) + 2. Also the number of sign patterns of vectors in the null-space of a totally L-matrix is obtained.
참고문헌 (9)
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