Displaying similar documents to “When does the inverse have the same sign pattern as the transpose?”

± sign pattern matrices that allow orthogonality

Yan Ling Shao, Liang Sun, Yubin Gao (2006)

Czechoslovak Mathematical Journal

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A sign pattern A is a ± sign pattern if A has no zero entries. A allows orthogonality if there exists a real orthogonal matrix B whose sign pattern equals A . Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for ± sign patterns with n - 1 ≤ N - ( A ) ≤ n + 1 to allow orthogonality.

Essential sign change numbers of full sign pattern matrices

Xiaofeng Chen, Wei Fang, Wei Gao, Yubin Gao, Guangming Jing, Zhongshan Li, Yanling Shao, Lihua Zhang (2016)

Special Matrices

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A sign pattern (matrix) is a matrix whose entries are from the set {+, −, 0} and a sign vector is a vector whose entries are from the set {+, −, 0}. A sign pattern or sign vector is full if it does not contain any zero entries. The minimum rank of a sign pattern matrix A is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of A. The notions of essential row sign change number and essential column sign change number are introduced...

On the inertia sets of some symmetric sign patterns

C. M. da Fonseca (2006)

Czechoslovak Mathematical Journal

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A matrix whose entries consist of elements from the set { + , - , 0 } is a sign pattern matrix. Using a linear algebra theoretical approach we generalize of some recent results due to Hall, Li and others involving the inertia of symmetric tridiagonal sign matrices.

Sign patterns of J-orthogonal matrices

Frank J. Hall, Zhongshan Li, Caroline T. Parnass, Miroslav Rozložník (2017)

Special Matrices

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This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator...

Basic Properties of Determinants of Square Matrices over a Field 1

Karol Pąk (2007)

Formalized Mathematics

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In this paper I present basic properties of the determinant of square matrices over a field and selected properties of the sign of a permutation. First, I define the sign of a permutation by the requirement [...] where p is any fixed permutation of a set with n elements. I prove that the sign of a product of two permutations is the same as the product of their signs and show the relation between signs and parity of permutations. Then I consider the determinant of a linear combination...

The inertia set of nonnegative symmetric sign pattern with zero diagonal

Yubin Gao, Yan Ling Shao (2003)

Czechoslovak Mathematical Journal

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The inertia set of a symmetric sign pattern A is the set i ( A ) = { i ( B ) ∣ B = B T ∈ Q ( A ) } , where i ( B ) denotes the inertia of real symmetric matrix B , and Q ( A ) denotes the sign pattern class of A . In this paper, a complete characterization on the inertia set of the nonnegative symmetric sign pattern A in which each diagonal entry is zero and all off-diagonal entries are positive is obtained. Further, we also consider the bound for the numbers of nonzero entries in the nonnegative symmetric sign patterns A with zero diagonal...