# IJPAM: Volume 32, No. 4 (2006)

LINEAR PRESERVER OF MATRIX MAJORIZATION

A.M. Hasani, M. Radjabalipour
Department of Mathematics
University of Kerman
Kerman, IRAN
e-mail: mohamad.h@graduate.uk.ac.ir
e-mail: radjab45@mail.uk.ac.ir

Abstract.An matrix is said to be matrix majorized from the left by an matrix , and write , if there exists an row stochastic matrix such that . Let denote the linear space of all real matrices. An operator is said to be a preserver of if whenever and . It is shown that a linear operator preserves if and only if there exist an permutation matrix , an real matrix , and real numbers and with , such that for all and, if , . Moreover, if satisfies the extra condition whenever , then for all and and are invertible.

Received: September 25, 2006

AMS Subject Classification: 15A04, 15A21, 15A30

Key Words and Phrases: row stochastic matrix, matrix majorization, linear preserver

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 32
Issue: 4