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Power indices of trace zero symmetric Boolean matrices

Bo Zhou (2004)

Discussiones Mathematicae - General Algebra and Applications

The power index of a square Boolean matrix A is the least integer d such that Ad is a linear combination of previous nonnegative powers of A. We determine the maximum power indices for the class of n×n primitive symmetric Boolean matrices of trace zero, the class of n×n irreducible nonprimitive symmetric Boolean matrices, and the class of n×n reducible symmetric Boolean matrices of trace zero, and characterize the extreme matrices respectively.

Preface

Carlos A. Coelho, Simo Puntanen (2013)

Discussiones Mathematicae Probability and Statistics

Product of exponentials and spectral radius of random k-circulants

Arup Bose, Rajat Subhra Hazra, Koushik Saha (2012)

Annales de l'I.H.P. Probabilités et statistiques

We consider n × n random k-circulant matrices with n → ∞ and k = k(n) whose input sequence {al}l≥0 is independent and identically distributed (i.i.d.) random variables with finite (2 + δ) moment. We study the asymptotic distribution of the spectral radius, when n = kg + 1. For this, we first derive the tail behaviour of the g fold product of i.i.d. exponential random variables. Then using this tail behaviour result and appropriate normal approximation techniques, we show that with appropriate scaling...

Product of operators and numerical range preserving maps

Chi-Kwong Li, Nung-Sing Sze (2006)

Studia Mathematica

Let V be the C*-algebra B(H) of bounded linear operators acting on the Hilbert space H, or the Jordan algebra S(H) of self-adjoint operators in B(H). For a fixed sequence (i₁, ..., iₘ) with i₁, ..., iₘ ∈ 1, ..., k, define a product of A ₁ , . . . , A k ∈ V by A ₁ * ⋯ * A k = A i ₁ ⋯ A i ₘ . This includes the usual product A ₁ * ⋯ * A k = A ₁ ⋯ A k and the Jordan triple product A*B = ABA as special cases. Denote the numerical range of A ∈ V by W(A) = (Ax,x): x ∈ H, (x,x) = 1. If there is a unitary operator U and a scalar μ satisfying μ m = 1 such that ϕ: V → V has the form A...

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