\(g\)-circulant solutions to the (0,1) matrix equation \(A^m=J_n\)

DOI10.1016/S0024-3795(01)00491-8zbMath0998.15015MaRDI QIDQ1347955

Qiao Li, Rui-Zhong Jia, Yaokun Wu

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/8/4/48/175/27/36/abstract.html

zbMATH Keywords

isomorphismmatrix equationde Bruijn digraphHall polynomialstandard factorization\((0,1)\) matrix\(g\)-circulantaddition setshifting parameter

Mathematics Subject Classification ID

Combinatorial aspects of matrices (incidence, Hadamard, etc.) (05B20) Matrix equations and identities (15A24) Matrices of integers (15B36)

Related Items (23)

Hoffman polynomials of nonnegative irreducible matrices and strongly connected digraphs ⋮ The spectral norms of \(g\)-circulant matrices with classical Fibonacci and Lucas numbers entries ⋮ Explicit form of the inverse matrices of tribonacci circulant type matrices ⋮ Unnamed Item ⋮ Orderly algorithm to enumerate central groupoids and their graphs ⋮ Rectangular groupoids and related structures ⋮ Graphs with the unique path property: Structure, cycles, factors, and constructions ⋮ Product of exponentials and spectral radius of random \(k\)-circulants ⋮ Poisson convergence of eigenvalues of circulant type matrices ⋮ An approach to solving \(A^{k}=J-I\) ⋮ The explicit identities for spectral norms of circulant-type matrices involving binomial coefficients and harmonic numbers ⋮ Central groupoids, central digraphs, and zero-one matrices \(A\) satisfying \(A^{2}=J\). ⋮ Invertibility and explicit inverses of circulant-type matrices with \(k\)-Fibonacci and \(k\)-Lucas numbers ⋮ Circulant type matrices with the sum and product of Fibonacci and Lucas numbers ⋮ Gaussian Fibonacci circulant type matrices ⋮ The invertibility, explicit determinants, and inverses of circulant and left circulant and \(g\)-circulant matrices involving any continuous Fibonacci and Lucas numbers ⋮ Generalized de Bruijn graphs ⋮ Limiting spectral distribution of random \(k\)-circulants ⋮ The underlying line digraph structure of some (0, 1)-matrix equations ⋮ Binary factorizations of the matrix of all ones ⋮ A note on certain matrices withh(x)– Fibonacci quaternion polynomials ⋮ On Jacobsthal and Jacobsthal-Lucas circulant type matrices ⋮ De Bruijn digraphs and affine transformations

Cites Work

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• On some solutions of \(A^k=dI+\lambda J\)
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