Irreducible powerful ray pattern matrices

DOI10.1016/S0024-3795(01)00436-0zbMath0994.15026MaRDI QIDQ1347932

Zhongshan Li, Jeffrey L. Stuart, Frank J. Hall

Publication date: 15 May 2002

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: http://www.mathematicsweb.org/pub/8/4/48/173/27/30/abstract.html

zbMATH Keywords

sign pattern matrixpowerful ray patternRay pattern matrixunambiguously defined powers

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (19)

Sign \(k\)-potent sign patterns and ray \(k\)-potent ray patterns that admit \(k\)-potence ⋮ A survey on bases of sign pattern matrices ⋮ The ray nonsingularity of certain uniformly random ray patterns ⋮ Forbidden structures for ray nonsingularity among cycle tree matrices without positive cycles ⋮ Matrices with totally signed powers. ⋮ Primitive zero-symmetric sign pattern matrices with zero diagonal attaining the maximum base ⋮ Periodic, reducible, powerful ray pattern matrices ⋮ Bounds on the bases of irreducible generalized sign pattern matrices ⋮ Primitive non-powerful sign pattern matrices with base 2 ⋮ Bounds on the \(k\)th multi-\(g\) base index of nearly reducible sign pattern matrices ⋮ Periodic, irreducible, powerful ray pattern matrices ⋮ The minimum upper bound on the first ambiguous power of an irreducible, nonpowerful ray or sign pattern ⋮ The base sets of quasi-primitive zero-symmetric sign pattern matrices with zero trace ⋮ Reducible powerful ray pattern matrices ⋮ BASE OF THE NON-POWERFUL SIGNED TOURNAMENT ⋮ Sign \(k\)-potent sign patterns and ray \(k\)-potent ray patterns that allow \(k\)-potence ⋮ THE PRIMITIVE BASES OF THE SIGNED CYCLIC GRAPHS ⋮ Irreducible, pattern \(k\)-potent ray pattern matrices ⋮ Reducible pattern \(k\)-potent ray pattern matrices

Cites Work

• Irreducible sign \(k\)-potent sign pattern matrices
• Reducible sign \(k\)-potent sign pattern matrices
• On the period and base of a sign pattern matrix
• Ray patterns of matrices and nonsingularity
• Extremal properties of ray-nonsingular matrices
• Irreducible, pattern \(k\)-potent ray pattern matrices
• Reducible pattern \(k\)-potent ray pattern matrices
• Eigenvalue distribution of certain ray patterns
• The structure of nonnegative cyclic matrices
• From real to complex sign pattern matrices
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