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Lehmer's conjecture for Hermitian matrices over the Eisenstein and Gaussian integers
Lehmer's conjecture Hermitian matrices Eisenstein and Gaussian integers Number Theory
2012/6/29
We solve Lehmer's problem for a class of polynomials arising from Hermitian matrices over the Eisenstein and Gaussian integers, that is, we show that all such polynomials have Mahler measure at least ...
A Trace Inequality for Positive Definite Matrices
Trace inequality positive definite matrices positive semidefinite matrices
2010/1/25
In this note we prove that when the following two conditions are met: (i) the matrices are structured as follows , , , (ii) , are positive definite matrices and , are positive semidefinite matric...