PERRON-FROBENIUS THEORY ON THE NUMERICAL RANGE FOR SOME CLASSES OF REAL MATRICES

نویسندگان

  • HAMID REZA AFSHIN DEPARTMENT OF MATHEMATICS, VALI-E-ASR UNIVERSITY OF RAFSANJAN, P. O. BOX 518, RAFSANJAN, IRAN
  • MOSTAFA ZANGIABADI DEPARTMENT OF MATHEMATICS, HORMOZGAN UNIVERSITY, P. O. BOX 3995, BANDAR ABBAS, IRAN
چکیده مقاله:

We give further results for Perron-Frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. We indicate two techniques for establishing the main theorem ofPerron and Frobenius on the numerical range. In the rst method, we use acorresponding version of Wielandt's lemma. The second technique involves graphtheory.

برای دانلود باید عضویت طلایی داشته باشید

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

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

perron-frobenius theory on the numerical range for some classes of real matrices

we give further results for perron-frobenius theory on the numericalrange of real matrices and some other results generalized from nonnegative matricesto real matrices. we indicate two techniques for establishing the main theorem ofperron and frobenius on the numerical range. in the rst method, we use acorresponding version of wielandt's lemma. the second technique involves graphtheory.

متن کامل

Perron-frobenius Theory for Complex Matrices

The purpose of this paper is to present a unified Perron-Frobenius Theory for nonnegative, for real not necessarily nonnegative and for general complex matrices. The sign-real spectral radius was introduced for general real matrices. This quantity was shown to share certain properties with the Perron root of nonnegative matrices. In this paper we introduce the sign-complex spectral radius. Agai...

متن کامل

Perron-Frobenius Type Results on the Numerical Range

We present results connecting the shape of the numerical range to intrinsic properties of a matrix A. When A is a nonnegative matrix, these results are to a large extent analogous to the Perron-Frobenius theory, especially as it pertains to irreducibility and cyclicity in the combinatorial sense. Special attention is given to polygonal, circular and elliptic numerical ranges. The main vehicles ...

متن کامل

Notes on the Perron-frobenius Theory of Nonnegative Matrices

By a nonnegative matrix we mean a matrix whose entries are nonnegative real numbers. By positive matrix we mean a matrix all of whose entries are strictly positive real numbers. These notes give the core elements of the Perron-Frobenius theory of nonnegative matrices. This splits into three parts: (1) the primitive case (due to Perron) (2) the irreducible case (due to Frobenius) (3) the general...

متن کامل

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

15 صفحه اول

Generalized Perron-Frobenius Theorem for Nonsquare Matrices

The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. H...

متن کامل

منابع من

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

ذخیره در منابع من قبلا به منابع من ذحیره شده

{@ msg_add @}


عنوان ژورنال

دوره 2  شماره 2

صفحات  1- 15

تاریخ انتشار 2014-11-23

با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.

میزبانی شده توسط پلتفرم ابری doprax.com

copyright © 2015-2023