相关论文: Some numerical characteristics of Sylvester and Ha…

Some aspects and applications of $ \sigma$-models in particle and condensed matter physics are briefly reviewed.

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive…

Inequalities play important roles not only in mathematics, but also in other fields, such as economics and engineering. Even though many results are published on Hermite-Hadamard (H-H) type inequalities, new researcher to this fields often…

The numerical radius of a matrix is a scalar quantity that has many applications in the study of matrix analysis. Due to the difficulty in computing the numerical radius, inequalities bounding it have received a considerable attention in…

Isoparametric hypersurfaces and their application to special geometries

In the paper "Confinement of matroid representations to subsets of partial fields" (arXiv:0806.4487) we introduced the Hydra-k partial fields to study quinary matroids with inequivalent representations. The proofs of some results on these…

The symmetry properties of the dynamical matrix are well described in multiple classic textbooks. This short paper revisits the issue to demonstrate alternative form of dynamical matrix which explicitly shows its symmetry and reality in…

In this article, we provide some necessary and sufficient coefficients conditions for a harmonic mapping to be hereditarily spirallike. Also, we give growth estimate for certain harmonic hereditarily spirallike mappings. Moreover, we…

The calculation of physical quantities by lattice QCD simulations requires in some important cases the determination of the inverse of a very large matrix. In this article we describe how stochastic estimator methods can be applied to this…

We obtain a series transformation formula involving the classical Hermite polynomials. We then provide a number of applications using appropriate binomial transformations. Several of the new series involve Hermite polynomials and harmonic…

We give some very interesting matrices which are orthogonal over groups and, as far as we know, referenced, but in fact undocumented. This note is not intended to be published but available for archival reasons.

We review old and new properties of Hopf manifolds from the point of view of their analytic and metric structure.

We prove that if $A$ and $B$ are Hadamard matrices which are both of size $4 \times 4$ or $5 \times 5$ and in dephased form, then $tr(A) = tr(B)$ implies that $A$ and $B$ have the same eigenvalues, including multiplicity. We calculate…

We give a formula for matrix exponentials and partial fraction decompositions.

We discuss and prove a number of results for calculating characteristic cycles, or graded, enriched characteristic cycles. We concentrate particularly on results related to hypersurfaces.

We survey a variety of results about partially isometric matrices. We focus primarily on results that are distinctly finite-dimensional. For example, we cover a recent solution to the similarity problem for partial isometries. We also…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

The Clement or Sylvester-Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations.…

A classical approach to accurately estimating the covariance matrix \Sigma of a p-variate normal distribution is to draw a sample of size n > p and form a sample covariance matrix. However, many modern applications operate with much smaller…

Positivity properties of the Hadamard powers of the matrix $\begin{bmatrix}1+x_ix_j\end{bmatrix}$ for distinct positive real numbers $x_1,\ldots,x_n$ and the matrix $\begin{bmatrix}|\cos((i-j)\pi/n)|\end{bmatrix}$ are studied. In…