Let H0 be an arbitrary self-adjoint n × n matrix and H(n) be an n × n (random) Wigner matrix. We show that t 7→ Tr exp(H(n)−itH0) is positive definite in the average. This partially answers a long-standing conjecture. On the basis of asymptotic freeness our result implies that t 7→ τ(exp(a − itb)) is positive definite whenever the noncommutative random variables a and b are in free relation, wi...

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‎In this paper‎, ‎some algebraic and geometrical properties of the rank$-k$ numerical hulls of normal matrices are investigated‎. ‎A characterization of normal matrices whose rank$-1$ numerical hulls are equal to their numerical range is given‎. ‎Moreover‎, ‎using the extreme points of the numerical range‎, ‎the higher rank numerical hulls of matrices of the form $A_1 oplus i A_2$‎, ‎where $A_1...

Polymerase chain reaction (PCR) is commonly used for pathogen detection in clinical and environmental samples. These sample matrices often contain inhibitors of PCR, which is a primary reason for sample processing; however, the purification process is highly inefficient, becoming unacceptable at lower signature concentrations. One potential solution is direct PCR assessment without sample proce...

A generic method to develop a defect monitoring system for IC processes, A comparison of new and old algorithms for a mixture estimation problem, The numerical evaluation of the maximum-likelihood estimate of a subset of mixture proportions, [19] LOQO an efficient implementation of an interior-point method for large scale linear and/or quadratic programming problems, available via ftp://elib.zi...

Digital beam forming (DBF) and synthetic aperture interferometry (SAI) are signal processing techniques that mix the signals collected by an antenna array to obtain high-resolution images with aid of a computer. This note aims at comparing these two approaches from algebraic perspective illustrations simulations conducted microwaves frequencies within frame Soil Moisture Ocean Salinity (SMOS) m...

in this paper, the ultraspherical operational matrices of derivatives are constructed. based on these operational matrices, two numerical algorithms are presented and analyzed for obtaining new approximate spectral solutions of a class of linear and nonlinear lane-emden type singular initial value problems. the basic idea behind the suggested algorithms is basically built on transforming the eq...

In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.