Related papers: The common-submatrix Laplace expansion

Matrix conditions extend linear Mal'tsev conditions from Universal Algebra to exactness properties in Category Theory. Some can be stated in the finitely complete context while, in general, they can only be stated for regular categories. We…

In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…

This report formulates a conjectural combinatorial rule that positively expands Grothendieck polynomials into Lascoux polynomials. It generalizes one such formula expanding Schubert polynomials into key polynomials, and refines another one…

We show that some common and important global constraints like ALL-DIFFERENT and GCC can be decomposed into simple arithmetic constraints on which we achieve bound or range consistency, and in some cases even greater pruning. These…

The goal of this article is to compare the coefficients in the expansion of the permanent with those in the expansion of the determinant of a three-lines circulant matrix. As an application we prove a conjecture concerning the minimality of…

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra…

Dempster's covariance selection method is extended first to general nonsingular matrices and then to full rank rectangular matrices. Dempster observed that his completion solved a maximum entropy problem. We show that our generalized…

A necessary and sufficient condition is provided for the solvability of a binomial congruence with a composite modulus, circumventing its prime factorization. This is a generalization of Euler's Criterion through that of Euler's Theorem,…

Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…

We study a nonlinear decomposition of a positive definite matrix into two components: the inverse of another positive definite matrix and a symmetric matrix constrained to lie in a prescribed linear subspace. Equivalently, the inverse…

Under certain conditions, a symmetric unimodal continuous random variable $\xi$ can be represented as a scale mixture of the standard Normal distribution $Z$, i.e., $\xi = \sqrt{W} Z$, where the mixing distribution $W$ is independent of…

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…

We consider *-linear maps into a commutative C*-algebra C (X) of continuous functions on a locally compact Hausdorff space X with certain specified properties and prove two results: (1) an extension result for a class of *-linear maps Y -->…

Some recent papers formulated sufficient conditions for the decomposition of matrix variances. A statement was that if we have one or two observables, then the decomposition is possible. In this paper we consider an arbitrary finite set of…

We consider two evolution equations involving space fractional Laplace operator of order $0<s<1$. We first establish some existence and uniqueness results for the considered evolution equations. Next, we give some comparison theorems and…

In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices.…

The efficient inversion of matrix polynomials is a critical challenge in computational mathematics. We design a procedure to determine the inverse of matrices polynomial of multidimensional Laplace matrices. The method is based on…

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem.

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

In this paper, we obtain a classification theorem of $2$-dimensional complete Lagrangian self-expanders with constant squared norm of the second fundamental form in $\mathbb C^{2}$.