Related papers: Calculating Determinants of Block Matrices
If a macromolecule is described by curvilinear coordinates or rigid constraints are imposed, the equilibrium probability density that must be sampled in Monte Carlo simulations includes the determinants of different mass-metric tensors. In…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
We present a variation and generalization of a determinant evaluation of Wilf (math.CO/9809120). His result concerns a matrix whose entries are the coefficients of powers of a given power series; we replace the powers by repeated…
The use of quadratic residues to construct matrices with specific determinant values is a familiar problem with connections to many areas of mathematics and statistics. Our research has focused on using cubic residues to construct matrices…
In this paper, the discriminant of homogeneous polynomials is studied in two particular cases: a single homogeneous polynomial and a collection of n-1 homogeneous polynomials in n variables. In these two cases, the discriminant is defined…
This paper presents new approaches for finding the determinant and inverse of a matrix. The choice of pivot selection is kept arbitrary and can be made according to the users need. So the ill conditioned matrices can be handled easily. The…
For bivariate polynomials of degree $n\le 5$ we give fast numerical constructions of determinantal representations with $n\times n$ matrices. Unlike some other available constructions, our approach returns matrices of the smallest possible…
For any positive integer $n$, let ${\rm C}_{n}$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of ${\rm C}_{2}^{2} \rtimes C_{4}$.
The paper develops Newton's method of finding multiple eigenvalues with one Jordan block and corresponding generalized eigenvectors for matrices dependent on parameters. It computes the nearest value of a parameter vector with a matrix…
We give a formula that expresses the Hilbert series of one-sided ladder determinantal rings, up to a trivial factor, in form of a determinant. This allows the convenient computation of these Hilbert series. The formula follows from a…
A formula expressing the fermionic determinant (a large order polynomial) as an infinite product of smaller determinants is derived and discussed. These smaller determinants are of a fixed size, independent of the size of the lattice and…
An efficient method is proposed for computing the structure of Jordan blocks of a matrix of integers or rational numbers by exact computation. We have given a method for computing Jordan chains of a matrix with exact computation. However,…
We evaluate determinants of "spiral" matrices, which are matrices in which entries are spiralling from the centre of the matrices towards the outside, with prescribed increments from one entry to the next depending on whether one moves…
We evaluate four families of determinants of matrices, where the entries are sums or differences of generating functions for paths consisting of up-steps, down-steps and level steps. By specialisation, these determinant evaluations have…
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These…
Quantum Monte Carlo approaches based on the stochastic sampling of the determinant space have evolved to be powerful methods to compute the electronic states of molecules. These methods not only calculate the correlation energy at an…
The linear complete differential resultant of a finite set of linear ordinary differential polynomials is defined. We study the computation by linear complete differential resultants of the implicit equation of a system of $n$ linear…
This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the…
Given a system of n homogeneous polynomials in n variables which is equivariant with respect to the canonical actions of the symmetric group of n symbols on the variables and on the polynomials, it is proved that its resultant can be…