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Full-Text Articles in Physical Sciences and Mathematics
Sign Pattern Matrices That Require Almost Unique Rank, Assefa D. Merid
Sign Pattern Matrices That Require Almost Unique Rank, Assefa D. Merid
Mathematics Theses
A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrixA, the sign pattern class of A, denoted Q(A), is defined as { B : sgn(B)= A }. The minimum rank mr(A)(maximum rank MR(A)) of a sign pattern matrix A is the minimum (maximum) of the ranks of the real matrices in Q(A). Several results concerning sign patterns A that require almost …
Spectrally Arbitrary And Inertially Arbitrary Sign Pattern Matrices, Nilay Sezin Demir
Spectrally Arbitrary And Inertially Arbitrary Sign Pattern Matrices, Nilay Sezin Demir
Mathematics Theses
A sign pattern(matrix) is a matrix whose entries are from the set {+,-,0}. An n x n sign pattern matrix is a spectrally arbitrary pattern(SAP) if for every monic real polynomial p(x) of degree n, there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). An n x n pattern A is an inertialy arbitrary pattern(IAP) if (r,s,t) belongs to the inertia set of A for every nonnegative triple (r,s,t) with r+s+t=n. Some elementary results on these two classes of patterns are first exhibited. Tree sign patterns are …
Rational Realizations Of The Minimum Rank Of A Sign Pattern Matrix, Selcuk Koyuncu
Rational Realizations Of The Minimum Rank Of A Sign Pattern Matrix, Selcuk Koyuncu
Mathematics Theses
A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. The minimum rank of a sign pattern matrix A is the minimum of the rank of the real matrices whose entries have signs equal to the corresponding entries of A. It is conjectured that the minimum rank of every sign pattern matrix can be realized by a rational matrix. The equivalence of this conjecture to several seemingly unrelated statements are established. For some special cases, such as when A is entrywise nonzero, or the minimum rank of A is at most 2, or the minimum rank …