Open AccessLINEAR TRANSFORMATIONS WHICH MAP THE CLASS OF INVERSE M-MATRICES ONTO ITSELF
Author(s) -
Bit-Shun Tam,
Po-Hong Liou
Publication year - 1990
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.21.1990.4651
Subject(s) - mathematics , inverse , matrix (chemical analysis) , closure (psychology) , class (philosophy) , linear map , product (mathematics) , combinatorics , transformation matrix , generalized inverse , matrix multiplication , space (punctuation) , pure mathematics , transformation (genetics) , geometry , computer science , artificial intelligence , chemistry , biochemistry , kinematics , classical mechanics , quantum mechanics , market economy , physics , economics , gene , materials science , composite material , quantum , operating system
The purpose of this paper is to characterize those linear transformations on the space of $n \times n$ real matrices which map the class of $n \times n$ inverse $M$- matrices (or, the closure of this class) onto itself. As a by-product of our approach, we also obtain a sufficient condition for an inverse $M$-matrix (resp. $M$-matrix) to have all positive powers being inverse $M$-matrices (resp. $M$-matrices).