The Smith form of an integer matrix plays an important role in the study of algebraic group theory, homology group theory, systems theory, matrix equivalence, Diophantine systems, and control theory. Asymptotic complexity of the Smith form computation has been steadily improved in the past four decades. A group of algorithms for computing the Smith forms is available now. The best asymptotic al...

We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including entries of covariance matrix, entries of precision matrix, quadratic forms, log-determinant, eigenvalues in the Bayesian Gaussian covariance/precision matrix estim...

The LDI matrix is introduced in its full and shortened forms. As an analogy of the Pascal matrix for the bilinear transform, the LDI matrix serves to transform the coefficients of the transfer functions of continuousand discrete-time linear circuits which are connected by the LDI (Lossless Discrete Integration) transform. The basic properties of the LDI matrix are presented and a procedure of i...

matrix metalloproteinases (mmps) are a family of neutral proteinases that are important in normal development, cellular differentiation or migration, angiogenesis, neurogenesis, wound repair, and a wide range of pathological processes such as oxidative stress and neuroinflammation. mmps have been demonstrated to increase the permeability of the blood–brain barrier (bbb) by degrading the compone...

In the estimation of mean matrix in a multivariate normal distribution, generalized Bayes estimators with closed forms are provided, and sufficient conditions for their minimaxity derived relative to both scalar quadratic loss functions. The covariance also given forms, dominance properties discussed Stein function.

The conditions under which, multilinear forms (the symmetric case and the non symmetric case),can be written as a product of linear forms, are considered. Also we generalize a result due to S.Kurepa for 2n-functionals in a group G.

the purpose of the present study is to introduce the sequence space[{l_p}(e,delta) = left{ x = (x_n)_{n = 1}^infty : sum_{n = 1}^infty left| sum_{j in {e_n}} x_j - sum_{j in e_{n + 1}} x_jright| ^p < infty right},]where $e=(e_n)$ is a partition of finite subsets of the positive integers and $pge 1$. the topological properties and inclusion relations of this space are studied. moreover, the prob...

let $rin textbf{c}^{mtimes m}$ and $sin textbf{c}^{ntimes n}$ be nontrivial involution matrices; i.e., $r=r^{-1}neq pm~i$ and $s=s^{-1}neq pm~i$. an $mtimes n$ complex matrix $a$ is said to be an $(r, s)$-symmetric ($(r, s)$-skew symmetric) matrix if $ras =a$ ($ ras =-a$). the $(r, s)$-symmetric and $(r, s)$-skew symmetric matrices have a number of special properties and widely used in engi...