Displaying similar documents to “ ± sign pattern matrices that allow orthogonality”

When does the inverse have the same sign pattern as the transpose?

Carolyn A. Eschenbach, Frank J. Hall, Deborah L. Harrell, Zhongshan Li (1999)

Czechoslovak Mathematical Journal

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By a sign pattern (matrix) we mean an array whose entries are from the set { + , - , 0 } . The sign patterns A for which every real matrix with sign pattern A has the property that its inverse has sign pattern A T are characterized. Sign patterns A for which some real matrix with sign pattern A has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal...

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...

On block triangular matrices with signed Drazin inverse

Changjiang Bu, Wenzhe Wang, Jiang Zhou, Lizhu Sun (2014)

Czechoslovak Mathematical Journal

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The sign pattern of a real matrix A , denoted by sgn A , is the ( + , - , 0 ) -matrix obtained from A by replacing each entry by its sign. Let 𝒬 ( A ) denote the set of all real matrices B such that sgn B = sgn A . For a square real matrix A , the Drazin inverse of A is the unique real matrix X such that A k + 1 X = A k , X A X = X and A X = X A , where k is the Drazin index of A . We say that A has signed Drazin inverse if sgn A ˜ d = sgn A d for any A ˜ ∈ 𝒬 ( A ) , where A d denotes the Drazin inverse of A . In this paper, we give necessary conditions for some block triangular matrices...

On an extension of Fekete’s lemma

Inheung Chon (1999)

Czechoslovak Mathematical Journal

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We show that if a real n × n non-singular matrix ( n ≥ m ) has all its minors of order m - 1 non-negative and has all its minors of order m which come from consecutive rows non-negative, then all m th order minors are non-negative, which may be considered an extension of Fekete’s lemma.

G -space of isotropic directions and G -spaces of ϕ -scalars with G = O ( n , 1 , ℝ )

Aleksander Misiak, Eugeniusz Stasiak (2008)

Mathematica Bohemica

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There exist exactly four homomorphisms ϕ from the pseudo-orthogonal group of index one G = O ( n , 1 , ℝ ) into the group of real numbers ℝ 0 . Thus we have four G -spaces of ϕ -scalars ( ℝ , G , h ϕ ) in the geometry of the group G . The group G operates also on the sphere S n - 2 forming a G -space of isotropic directions ( S n - 2 , G , * ) . In this note, we have solved the functional equation F ( A * q 1 , A * q 2 , ⋯ , A * q m ) = ϕ ( A ) · F ( q 1 , q 2 , ⋯ , q m ) for given independent points q 1 , q 2 , ⋯ , q m ∈ S n - 2 with 1 ≤ m ≤ n and an arbitrary matrix A ∈ G considering each of all four homomorphisms. Thereby we have determined all equivariant mappings...