Advanced Determinant Calculus

نویسنده

  • C KRATTENTHALER
چکیده

The purpose of this article is threefold First it provides the reader with a few useful and e cient tools which should enable her him to evaluate nontrivial de terminants for the case such a determinant should appear in her his research Second it lists a number of such determinants that have been already evaluated together with explanations which tell in which contexts they have appeared Third it points out references where further such determinant evaluations can be found Introduction Imagine you are working on a problem As things develop it turns out that in order to solve your problem you need to evaluate a certain determinant Maybe your determinant is

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Advanced Determinant Calculus: a Complement

This is a complement to my previous article “Advanced Determinant Calculus” (Séminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441– ...

متن کامل

The determinant

A (mostly) self-contained introduction to the determinant aimed at advanced undergraduates, written for the Math 350H class at Rutgers spring semester of 2017. Most of the material is taken from [1, 2], but it has been substantially reorganized. The goal of this article is to present an organized and motivated discussion of the abstract definition of the determinant and its most basic propertie...

متن کامل

The determinant of the Malliavin matrix and the determinant of the covariance matrix for multiple integrals

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 for couples of random vectors of multiple integrals. In particular, if the multiple integrals are of the same order and this order is at most 4, we prove that ...

متن کامل

Instanton calculus for the self-avoiding manifold model

We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold (SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the ǫ-expansion for this problem. For that purpose, we develop the methods inspired from instanton calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) ...

متن کامل

New Variational Method of Grid Generation with Prescribed Jacobian Determinant and Prescribed Curl

Adaptive grid generation is an active research topic for numerical solution of differential equations. In this paper, we propose a variational method which generates transformations with prescribed Jacobian determinant and curl. Then we use this transformation to achieve adaptive grid generation task.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999