Related papers: Transformations preserving the effective spectral …
For an exact quantitative description of spectral properties in the theory of synchrotron radiation, the concept of effective spectral width is introduced. In the classical theory, numeric calculations of effective spectral width (using an…
We determine the structure of linear maps on complex (real) square matrices sending unitary (orthogonal) matrices to multiples of unitary (orthogonal) matrices. The result is used to determine the linear preservers of matrix pairs…
We characterize real and complex functions which, when applied entrywise to square matrices, yield a positive definite matrix if and only if the original matrix is positive definite. We refer to these transformations as sign preservers.…
The possible spatial transformation properties of tetrons are discussed.
In this paper we determine those bijective maps of the set of all positive definite $n\times n$ complex matrices which preserve a given Bregman divergence corresponding to a differentiable convex function that satisfies certain conditions.…
The matrix inversion is an interesting topic in algebra mathematics. However, to determine an inverse matrix from a given matrix is required many computation tools and time resource if the size of matrix is huge. In this paper, we have…
The partial transpose of a block matrix M is the matrix obtained by transposing the blocks of M independently. We approach the notion of partial transpose from a combinatorial point of view. In this perspective, we solve some basic…
We suggest a way to manipulate electromagnetic wave by introducing a rotation mapping of coordinates that can be realized by a specific transformation of permittivity and permeability of a shell surrounding an enclosed domain. Inside the…
The transition-matrix ($T$-matrix) approach provides a general formalism to study scattering problems in various areas of physics, including acoustics (scalar fields) and electromagnetics (vector fields), and is related to the theory of the…
The rational Landen transformation is a map on the space of coefficients of a rational integrand that preserves the value of the integral. We provide a family of these transformations that apply to rational integrands on the whole line.…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
The aim of this article is to present a brief overview of spectral perturbation theory for matrices, bounded linear operators and holomorphic operator-valued functions. We focus on bounds for perturbed eigenvalues, eigenvectors and…
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…
We prove that all injective maps on positive complex matrices which preserve order and shrink spectrum are implemented by unitary or antiunitary conjugations. We show by counterexamples that all assumptions are indispensable. The result…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is…
Transformation optics is a powerful tool to design various novel devices, such as invisibility cloak. Fantastic effects from this technique are usually accompanied with singular mappings, resulting in challenging implementations and narrow…
A path integral formulation is developed to study the spectrum of radiation from a perfectly reflecting (conducting) surface. It allows us to study arbitrary deformations in space and time. The spectrum is calculated to second order in the…
The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…