Related papers: Transformations preserving the effective spectral …
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
By applying the optical nanocircuit concepts to metasurfaces, we propose an effective route to locally control light transmission over a deeply subwavelength scale. This concept realizes the optical equivalent of a transmitarray, whose use…
Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the…
The effects of coherence of quantum transitions and the interference of resonant nonlinear optical processes on the spectra of absorption, amplification, and nonlinear-optical generation are considered. The most favorable conditions are…
We show that spectral problems for periodic operators on lattices with embedded defects of lower dimensions can be solved with the help of matrix-valued integral continued fractions. While these continued fractions are usual in the…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
Semipositive matrices (matrices that map at least one nonnegative vector to a positive vector) and minimally semipositive matrices (semipositive matrices whose no column-deleted submatrix is semipositive) are well studied in matrix theory.…
In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…
The lower spectral radius of a set of $d \times d$ matrices is defined to be the minimum possible exponential growth rate of long products of matrices drawn from that set. When considered as a function of a finite set of matrices of fixed…
An $n \times n$ matrix $A$ with real entries is said to be Schur stable if all the eigenvalues of $A$ are inside the open unit disc. We investigate the structure of linear maps on $M_n(\mathbb{R})$ that preserve the collection $\mathcal{S}$…
We develop a procedure for determining whether a square complex matrix is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. Our approach has several advantages over existing methods. We discuss these differences and…
If we take a superintegrable Stackel system and make variables "faster" or "slower", that is equivalent to a trivial transformation of the Stackel matrix and potentials, then we obtain an infinite family of superintegrable systems with…
In this paper, we give the spectrum of a matrix by using the quotient matrix, then we apply this result to various matrices associated to a graph and a digraph, including adjacency matrix, (signless) Laplacian matrix, distance matrix,…
Under suitable hypotheses on the ground field and on the matrix $M$, we discuss existence, uniqueness and properties of some additive decompositions of $M$ and of its image through a convergent series.
Spectral measures give rise to a natural harmonic analysis on the unit disc via a boundary representation of a positive matrix arising from a spectrum of the measure. We consider in this paper the reverse: for a positive matrix in the Hardy…
Owing to success in the data-rich domain of natural images, Transformers have recently become popular in medical image segmentation. However, the pairing of Transformers with convolutional blocks in varying architectural permutations leaves…
This is the second article in a series of two which report on a matrix approach for ultrasound imaging in heterogeneous media. This article describes the quantification and correction of aberration, i.e. the distortion of an image caused by…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
Let H be a complex Hilbert space, B(H) and S(H) be the spaces of all bounded operators and all self-adjoint operators on H, respectively. We give the concrete forms of the maps on B(H) and also S(H) which preserve the spectrum of certain…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…