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Eigenvalues of products of unitary matrices and Lagrangian involutions
Unitary representations Parabolic bundles Lagrangian involutions
2015/12/17
This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
The q-Gelfand-Tsetlin graph, Gibbs measures and q-Toeplitz matrices
The q-Gelfand-Tsetlin graph Gibbs measures
2010/11/12
The problem of the description of finite factor representations of the infinite-dimensional unitary group, investigated by Voiculescu in 1976, is equivalent to the description of all totally positive...
Relatively Prime Polynomials and Nonsingular Hankel Matrices over Finite Fields
Relatively Prime Polynomials Nonsingular Hankel Matrices
2010/11/12
The probability for two monic polynomials of a positive degree n with coefficients in the finite field F_q to be relatively prime turns out to be identical with the probability for an n x n Hankel ma...
Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
Cyclotomic Matrices Graphs imaginary quadratic fields
2010/11/18
We determine all Hermitian $\mathcal{O}_{\Q(\sqrt{d})}$-matrices for which every eigenvalue is in the interval [-2,2], for each d in {-2,-7,-11,-15\}. To do so, we generalise charged signed graphs to...
A complete algorithm for determining copositive matrices
A complete algorithm for determining copositive matrices math
2010/11/15
In this paper, we present a complete algorithm called COPOMATRIX for determining the copositivity of an $n\times n$ matrix. The core of this algorithm is decomposition theorem, which is used to deal ...
The Construction of Maximum Independent Set of Matrices via Clifford Algebras
Hurwitz Theorem Clifford algebras maximum independent set of matrices
2010/2/26
In [1], [2] and [6] the maximum number of some special type n x n matrices with elements in F whose nontrivial linear combinations with real coefficients are nonsingular is studied where F is the rea...