Quantale矩阵的行列式的若干性质

基于Q uan ta le矩阵的定义,本文讨论了Q uan ta le矩阵的行列式的若干性质。在交换Q uan ta le情形下,得到AB≥A B,AB≤A B,AA*≤A,其中A*表示Q uan ta le上的矩阵A的伴随矩阵。     

格矩阵的行列式与伴随矩阵

研究了格矩阵的行列式与伴随矩阵,给出了它们的一些代数性质,同时给出了由一个格矩阵构造一个传递矩阵的方法.     

范德蒙行列式推广形式的多项式证法

本文给出了范德蒙行列式推广形式的多项式证明，其方法不同于文［１］的定理１证明方法。     

Wronsky行列式及其一阶微分的关系

证明了n阶行列式一阶微分为其逐次微分之和,进而得到了Wronsky行列式及其一阶微分的关系．     

实四元数矩阵行列式函数的几点注记

分别对实四元数矩阵理论中出现的几种行列式函数在三个初等变换下的改变性作一些讨论,得出几种满足一定性质的行列式函数的不存在性或唯一存在性。     

On the Relation Between the Determinant and the Permanent on Symmetric Matrices

Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ? 3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied.     

On the Relation Between the Determinant and the Permanent on Symmetric Matrices

Let H n ( F ) be the space of n -square symmetric matrices over the field F . We generalize the main result of [M.H. Lim (1979). A note on the relation between the determinant and the permanent. Linear and Multilinear Algebra , 7 , 145-147], proving that the determinant is not convertible into the permanent on H n ( F ), provided that n ≥3, F has at least n elements and the characteristic of F is not 2. The case n = 2 is also studied.     

计算周期三对角矩阵行列式和逆矩阵的新算法

给出了一种计算周期三对角矩阵行列式和逆矩阵的新递推算法,它们的运算复杂度分别为O(n)和O(n2),该算法是文献[5]和[6]中相关算法的拓广.     

The Dixmier trace and asymptotics of zeta functions

We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the trace of the heat semigroup. We prove our results in a general semi-finite von Neumann algebra. We find for p>1 that the asymptotics of the zeta function determines an ideal strictly larger than Lp,∞ on which the Dixmier trace may be defined. We also establish stronger versions of other results on Dixmier traces and zeta functions.     

The Dirichlet divisor problem,traces and determinants for complex powers of the twisted bi-Laplacian

Estimating the counting function for the eigenvalues of the twisted bi-Laplacian leads to the Dirichlet divisor problem, which is then used to compute the trace of the heat semigroup and the Dixmier trace of the inverse of the twisted bi-Laplacian. The zeta function regularizations of the traces and determinants of complex powers of the twisted bi-Laplacian are computed. A formula for the zeta function regularizations of determinants of heat semigroups of complex powers of the twisted bi-Laplacian is given.     

Positivity of matrices with generalized matrix functions

Using an elementary fact on matrices we show by a unified approach the positivity of a partitioned positive semidefinite matrix with each square block replaced by a compound matrix, an elementary symmetric function or a generalized matrix function. In addition, we present a refined version of the Thompson determinant compression theorem.     

迹与行列式的相互表示

应用牛顿恒等式,得到矩阵的特征值的对称多项式与等幂和之间的关系,以此为基础给出行列式的迹表示,另由克莱姆法则导出迹的行列式表示。     

A Priori Estimations of a Global Homotopy Residue Continuation Method

This work is concerned with the a priori estimations of a global homotopy residue continuation method starting from a disjoint initial guess. Explicit conditions ensuring the quadratic convergence of the underlying Newton–Raphson algorithm are proved.     

关于正交矩阵特征值与行列式的两个定理

以两种证明思路给出了正交矩阵特征值与行列式关系的定理,并在此基础之上提出了对称正交矩阵行列式的迹定理.     

η Forms and determinant lines

We construct a canonical zeta function (Quillen) connection on the determinant line bundle for a family of APS elliptic boundary value problems and show that its curvature is the 2-form component of a relative eta form.     

A Note on Residue Formulas for the Euler Class of Sphere Fibrations

This paper presents a definition of residue formulas for the Euler class of cohomology-oriented sphere fibrations ξ. If the base of ξ is a topological manifold, a Hopf index theorem can be obtained and, for the smooth category, a generalization of a residue formula is derived for real vector bundles given in [2].     

ζ-function and heat kernel formulae

We present a systematic study of asymptotic behaviour of (generalised) ζ-functions and heat kernels used in noncommutative geometry and clarify their connections with Dixmier traces. We strengthen and complete a number of results from the recent literature and answer (in the affirmative) the question raised by M. Benameur and T. Fack (2006) [1].     

The Flagged Cauchy Determinant

We consider a flagged form of the Cauchy determinant, for which we provide a combinatorial interpretation in terms of nonintersecting lattice paths. In combination with the standard determinant for the enumeration of nonintersecting lattice paths, we are able to give a new proof of the Cauchy identity for Schur functions. Moreover, by choosing different starting and end points for the lattice paths, we are led to a lattice path proof of an identity of Gessel which expresses a Cauchy-like sum of Schur functions in terms of the complete symmetric functions.     

The Behavior of Polylogarithms at z = 1

This note discusses the analytic behavior of the general polylogarithm Li _s (z) at the singularity z = 1. We consider both integer and complex values for s. Using these results, we derive yet another way of extending the Riemann zeta function to the entire plane.     

The newsvendor problem under multiplicative background risk

This note studies the single-period newsvendor problem when the newsvendor faces a multiplicative neutral independent background risk in an expected utility framework. It is shown that multiplicative risk vulnerability is a sufficient condition to guarantee a decrease in the optimal order. A weaker sufficient condition which has more interpretability is also provided and discussed. This result sheds light on situations where exchange, tax or inflation rates risks, which apply multiplicatively to the final wealth, are at work.