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

**LINEAR PRESERVER OF MATRIX MAJORIZATION**

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