Related papers: Corners of normal matrices

Using a notation of corner between edges when graph has a fixed rotation, i.e. cyclical order of edges around vertices, we define combinatorial objects - combinatorial maps as pairs of permutations, one for vertices and one for faces.…

Many interesting examples of complex Hadamard matrices $H\in M_N(\mathbb C)$ can be put, up to the standard equivalence relation for such matrices, in bistochastic form. We discuss here this phenomenon, with a number of computations for…

Let $H_{n}^{+}(\mathbb{R})$ be the cone of all positive semidefinite $n\times n$ real matrices. We describe the form of all surjective maps on $H_{n}^{+}(\mathbb{R}) $, $n\geq 3$, that preserve the minus partial order in both directions.

We deform block triangular Jacobi matrices appearing in geometry, look at multi-scale Barycentric limits of geometries and droplet boundary manifolds in Potts networks.

The ground state of colloidal magnetic particles in a modulated channel are investigated as function of the tilt angle of an applied magnetic field. The particles are confined by a parabolic potential in the transversal direction while in…

We study the cone of completely positive (cp) matrices for the first interesting case $n = 5$. This is a semialgebraic set, which means that the polynomial equalities and inequlities that define its boundary can be derived. We characterize…

We consider Hamilton cycles in the random digraph $D_{n,m}$ where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in the same direction as we traverse the cycle. We show that if…

We analyse the normal quotient structure of several infinite families of finite connected edge-transitive, four-valent oriented graphs. These families were singled out by Marusic and others to illustrate various different internal…

The main focus of this work is the study of several cones relating the eigenvalues or singular values of a matrix to those of its off-diagonal blocks.

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone…

For a positive linear map F and a normal matrix N, we show that |F(N)| is bounded by some simple linear combinations in the unitary orbit of F(|N|). Several elegant sharp inequalities are derived, especially for the Schur product.

In this paper, we give upper and lower bounds for the spectral norms of r-circulant matrices with the generalized bi-periodic Fibonacci numbers. Moreover, we investigate the eigenvalues and determinants of these matrices.

Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of…

Several subadditivity results and conjectures are given for matrices (or operators), block-matrices, concave functions and norms.

We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case:…

We study categories of matrix factorizations. These categories are defined for any regular function on a suitable regular scheme. Our paper has two parts. In the first part we develop the foundations; for example we discuss derived direct…

Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.

The continuity of the core inverse and the dual core inverse is studied in the setting of C*-algebras. Later, this study is specialized to the case of bounded Hilbert space operators and to complex matrices. In addition, the…

As is well known, any complex cyclic matrix $A$ is similar to the unique companion matrix associated with the minimal polynomial of $A$. On the other hand, a cyclic matrix over a division ring $\mathbb F$ is similar to a companion matrix of…

In this paper, we introduce a natural geometric extension of the partition function. More precisely, we investigate the problem of counting partitions of a rectangle into rectangular blocks with integer sides. Here, two partitions of a…