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Irreducibility of associated matrices

Abstract

AbstractFor an n by n matrix A, let K(A) be the associated matrix corresponding to a permutation group (of degree m) and one of its characters. Let Dr(A) be the coefficient of xm−r in K(A+xI). If A is reducible, then Dr(A) is reducible. If A is irreducible and the character is identically one, then D1(A) is irreducible. If A is row stochastic and the character is identically one, then Dr(A) is essentially row stochastic. Finally, the results motivate the definition of group induced diagraphs

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