Related papers: Permanental Vectors

The rank of an n x n matrix A is equal to the size of its largest square submatrix with a nonzero determinant, and it can be computed in O(n^2.37) time. Analogously, the size of the largest square submatrix with nonzero permanent is defined…

A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…

We consider generalized gradients in the general context of $G$-structures. They are natural first order differential operators acting on sections of vector bundles associated to irreducible $G$-representations. We study their geometric…

Quiver representations arise naturally in many areas across mathematics. Here we describe an algorithm for calculating the vector space of sections, or compatible assignments of vectors to vertices, of any finite-dimensional representation…

A definition of $d$--dimensional $n$--Meixner random vectors is given first. This definition involves the commutators of their semi--quantum operators. After that we will focus on the $1$-Meixner random vectors, and derive a system of $d$…

A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear…

We give a sufficient condition for the existence of a quadratic exponential vector with test function in L2(Rd) ? L?(Rd). We prove the linear independence and totality, in the quadratic Fock space, of these vectors. Using a technique…

In this article, we study the ideal generated by $2\times 2$ permanents of a symmetric matrix. We denote this ideal by $P_2(X)$ where $X$ is a symmetric matrix. We compute a Gr\"obner basis, dimension, depth, minimal primes, and a primary…

We review the quadratic form of the Laplace operator in 3 dimensions in spehrical coordinates which acts on the transverse components of vector functions. Operators, acting on the parametrizing functions of one of the transverse components…

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…

In this paper we provide an identity between determinant and generalized matrix function. Also, a criterion of positive semi-definite matrices affirming the permanent dominant conjecture is given. As a consequence, infinitely many infinite…

The explicit construction of direct and inverse Fourier's vector transform with discontinuous coefficients is presented. The technique of applying Fourier's vector transform with discontinuous coefficients for solving problems of…

Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…

A generalization of fractional vector calculus as a self-consistent mathematical theory is proposed to take into account a general form of non-locality in kernels of fractional vector differential and integral operators. Self-consistency…

It is generalized Weyl conformal curvature tensor in the case of a conformal mappings of a generalized Riemannian space in this paper. Moreover, it is found universal generalizations of it without any additional assumption. A method used in…

We investigate determinants of random unitary pencils (with scalar or matrix coefficients), which generalize the characteristic polynomial of a single unitary matrix. In particular we examine moments of such determinants, obtained by…

VSI (`vanishing scalar invariant') spacetimes have zero values for all total scalar contractions of all polynomials in the Riemann tensor and its covariant derivatives. However, there are other ways of concocting local scalar invariants…

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three infinite dimensional, irreducible, admissible representations of G, the space of G-invariant linear forms has dimension 0 or 1. When a non-zero linear…

We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…

We deploy algebraic complexity theoretic techniques for constructing symmetric determinantal representations of for00504925mulas and weakly skew circuits. Our representations produce matrices of much smaller dimensions than those given in…