Related papers: Transformations preserving the effective spectral …
Optimal matrices for problems involving the matrix numerical radius often have fields of values that are disks, a phenomenon associated with partial smoothness. Such matrices are highly structured: we experiment in particular with the…
Digital array orthogonal transformations that can be presented as a decomposition over basis items or basis images are considered. The orthogonal transform provides digital data scattering, a process of pixel energy redistributing, that is…
Finding reliably and efficiently the spectrum of the resonant states of an optical system under varying parameters of the medium surrounding it is a technologically important task, primarily due to various sensing applications.…
In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of…
This is a version of a part of the book ``Transformations of Grassman Spaces'' (in progress). We study transformations of Grassman spaces preserving certain geometrical constructions related to buildings. The next part will be devoted to…
A scattering transform defines a locally translation invariant representation which is stable to time-warping deformations. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
This article is a short review on the relationship between convergent matrix integrals, formal matrix integrals, and combinatorics of maps. We briefly summarize results developed over the last 30 years, as well as more recent discoveries.…
We discuss permutation representations which are obtained by the natural action of $S_n \times S_n$ on some special sets of invertible matrices, defined by simple combinatorial attributes. We decompose these representations into…
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to…
In this short note, we classify the degree-inverting involution on the full square and triangular matrices.
Isospectral transformations (IT) of matrices and networks allow for compression of either object while keeping all the information about their eigenvalues and eigenvectors.We analyze here what happens to generalized eigenvectors under…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We consider infinite matrices obtained by restricting Hardy integral kernels to natural numbers. For a suitable class of Hardy kernels we describe the absolutely continuous spectrum, the essential spectrum and the asymptotic spectral…
We exhibit several transformations of surfaces in R^4. First, one that takes a flat surface and gets a surface with flat normal bundle; then, one that takes a surface with flat normal bundle and gets a flat surface; finally, a one-parameter…
Transition radiation is a fundamental process of light emission and occurs whenever a charged particle moves across an inhomogeneous region. One feature of transition radiation is that it can create light emission at arbitrary frequency…
For a positive integer $n$ let $\mathcal{X}_n$ be either the algebra $M_n$ of $n \times n$ complex matrices, the set $N_n$ of all $n \times n$ normal matrices, or any of the matrix Lie groups $\mathrm{GL}(n)$, $\mathrm{SL}(n)$ and…
When we speak about parametric programming, sensitivity analysis, or related topics, we usually mean the problem of studying specified perturbations of the data such that for a given optimization problem some optimality criterion remains…
The homogeneous transform has many practical applications outside the realm of mathematics, for instance to represent the proportions of several chemical substances. We aim here to present results about the transformation of measures, which…
We study various convex functions on $R^n$ associated with positive definite matrices. This yiels some exotic Holder matrix inequalities.