IJPAM: Volume 32, No. 4 (2006)
Department of Mathematics
University of Kerman
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