Related papers: On the Cayley-Hamilton Theorem for Supermatrices
In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the…
The purpose of this paper is to present a characterization of sequentially Cohen-Macaulay modules in terms of its Hilbert coefficients with respect to distinguished parameter ideals. The formulas involve arithmetic degrees. Among…
We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the…
Renteln proved that the eigenvalues of the distance matrix of a Cayley graph of a real reflection group with respect to the set of all reflections are integral and provided a combinatorial formula for some such spectra. We prove the…
The aim of this paper is to study generating functions for the coefficients of the classical superoscillatory function associated with weak measurements. We also establish some new relations between the superoscillatory coefficients and…
We establish the Hodge conjecture for the top dimensional cohomology group with integer coefficients of any $q$-complete complex manifold $X$ with $q<\dim X$. This holds in particular for the complement $X=\mathbb{C}\mathbb{P}^n\setminus A$…
We exhibit a Cayley-Hamilton trace identity for $2\times2$ matrices with entries in a ring $R$ satisfying $[[x,y],[x,z]]=0$ and 1/2 \in R$.
In this paper, we prove the conjecture for the coefficients of the two variable generating function used in our previous paper. The conjecture was tested numerically before, but its proof was lacking up to now.
Supertropical matrix theory was investigated in [6], whose terminology we follow. In this work we investigate eigenvalues, characteristic polynomials and coefficients of characteristic polynomials of supertropical matrices and their powers,…
The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant…
We derive the general supertrace formula for a system with $N$ chiral superfields and one nilpotent chiral superfield in global and local supersymmetry. The nilpotent multiplet is realized by taking the scalar-decoupling limit of a chiral…
The Clifford-Hermite and the Clifford-Gegenbauer polynomials of standard Clifford analysis are generalized to the new framework of Clifford analysis in superspace in a merely symbolic way. This means that one does not a priori need an…
It is known that in the case of hyperelliptic curves the Shafarevich conjecture can be made effective, i.e., for any number field k and any finite set of places S of k, one can effectively compute the set of isomorphism classes of…
In this work we provide a novel approach for computing the coefficients of the characteristic polynomial of a square matrix. We demonstrate that each coefficient can be efficiently represented by a set of circle graphs. Thus, one can employ…
Semidefinite programming optimises a linear objective function over a spectrahedron, and is one of the major advances of mathematical optimisation. Spectrahedra are described by linear pencils, which are linear matrix polynomials with…
In this paper, the Conley conjecture, which were recently proved by Franks and Handel \cite{FrHa} (for surfaces of positive genus), Hingston \cite{Hi} (for tori) and Ginzburg \cite{Gi} (for closed symplectically aspherical manifolds), is…
We compare previously found finite-dimensional matrix and integral operator realizations of the Bailey lemma employing univariate elliptic hypergeometric functions. With the help of residue calculus we explicitly show how the integral…
We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a "one-line" combinatorial proof of the unimodality of the binomial coefficients. Other examples include…
One of the equivalent formulations of the Kadison-Singer problem which was resolved in 2013 by Marcus, Spielman and Srivastava, is the "paving conjecture". Roughly speaking, the paving conjecture states that every positive semi-definite…
We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a…