On Two Brownian–type Classes of Matrices with Explicit Hessenberg Inverses

نویسنده

  • F. N. Valvi
چکیده

The present paper constitutes an investigation on two twin classes of matrices, which result as Hadamard products of already known classes of matrices. The classes under consideration have Brownian form, which is defined by 3n − 1 parameters. Their inverses are matrices of lower Hessenberg form, the elements of which can be expressed analytically by these parameters. The explicit forms of the inverses and determinants of the two classes are given and the numerical complexity on the inverse evaluation is considered.

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

Inverses of regular Hessenberg matrices

A new proof of the general representation for the entries of the inverse of any unreduced Hessenberg matrix of finite order is found. Also this formulation is extended to the inverses of reduced Hessenberg matrices. Those entries are given with proper Hessenbergians from the original matrix. It justifies both the use of linear recurrences for such computations and some elementary properties of ...

متن کامل

An implicit Q-theorem for Hessenberg-like matrices

The implicit Q-theorem for Hessenberg matrices is a widespread and powerful theorem. It is used in the development of for example implicit QR-algorithms to compute the eigendecomposition of Hessenberg matrices. Moreover it can also be used to prove the essential uniqueness of orthogonal similarity transformations of matrices to Hessenberg form. The theorem is also valid for symmetric tridiagona...

متن کامل

Brownian motion and random matrices

This workshop, sponsored by AIM and NSF, was devoted to β-generalizations of the classical ensembles in random matrix theory. Recent advances have put stochastic methods on center stage, thus explaining the workshop title ‘Brownian motion and random matrices’. One recalls that a viewpoint on classical random matrix theory, generalizing Dyson’s three fold way, is that physically relevant ensembl...

متن کامل

More on the Fibonacci Sequence and Hessenberg Matrices

Five new classes of Fibonacci-Hessenberg matrices are introduced. Further, we introduce the notion of two-dimensional Fibonacci arrays and show that three classes of previously known Fibonacci-Hessenberg matrices and their generalizations satisfy this property. Simple systems of linear equations are given whose solutions are Fibonacci fractions.

متن کامل

Schur Flows for Orthogonal Hessenberg Matrices

We consider a standard matrix ow on the set of unitary upper Hessenberg matrices with nonnegative subdiagonal elements. The Schur parametrization of this set of matrices leads to ordinary diier-ential equations for the weights and the parameters that are analogous with the Toda ow as identiied with a ow on Jacobi matrices. We derive explicit diierential equations for the ow on the Schur paramet...

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 2002