相关论文: Evaluating Two Determinants

Rank two parametric perturbations of operators and matrices are studied in various settings. In the finite dimensional case the formula for a characteristic polynomial is derived and the large parameter asymptotics of the spectrum is…

This work involves the usage of various NLP models to predict the winner of a particular judgment by the means of text extraction and summarization from a judgment document. These documents are useful when it comes to legal proceedings. One…

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…

In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.

In this paper, we give the first and second fundamental theorems of invariant theory for certain invariant rings whose generators are expressed by circulant determinants.

I present a partly pedagogic discussion of the Gel'fand-Yaglom formula for the functional determinant of a one-dimensional, second order difference operator, in the simplest settings. The formula is a textbook one in discrete…

In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found

We investigate invertible matrices over finite additively idempotent semirings. The main result provides a criterion for the invertibility of such matrices. We also give a construction of the inverse matrix and a formula for the number of…

Resultants and Gr\"obner bases are crucial tools in studying polynomial elimination theory. We investigate relations between the variety of the resultant of two polynomials and the variety of the ideal they generate. Then we focus on the…

The comparison between discriminative and generative classifiers has intrigued researchers since Efron's seminal analysis of logistic regression versus discriminant analysis. While early theoretical work established that generative…

The article considers arrowhead and diagonal-plus-rank-one matrices in F^(nxn) where F in R,C or H. H is a non-commutative field of quaternions. We give unified formulas for fast matrix-vector multiplications, determinants, and inverses for…

In this article, we evaluate determinants of block hook matrices, which are block matrices consist of hook matrices. In particular, we deduce that the determinant of a block hook matrix factorizes nicely. In addition we give a combinatorial…

This paper deals with eigenvalues and eigenvectors of bicomplex linear operators defined on bicomplex space. We investigate the properties of these operators in the context of eigenvalues and eigenvectors, along with some relevant theorems.…

Effective computation of resultants is a central problem in elimination theory and polynomial system solving. Commonly, we compute the resultant as a quotient of determinants of matrices and we say that there exists a determinantal formula…

Robust classification algorithms have been developed in recent years with great success. We take advantage of this development and recast the classical two-sample test problem in the framework of classification. Based on the estimates of…

This paper studies the problem of decomposing a low-rank matrix into a factor with binary entries, either from $\{\pm 1\}$ or from $\{0,1\}$, and an unconstrained factor. The research answers fundamental questions about the existence and…

In an earlier paper, we discussed the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…

We consider different choice procedures such as scoring rules, rules, using majority relation, value function and tournament matrix, which are used in social and multi-criteria choice problems. We focus on the study of the properties that…

A well-known problem in Malliavin calculus concerns the relation between the determinant of the Malliavin matrix of a random vector and the determinant of its covariance matrix. We give an explicit relation between these two determinants…

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually…