LINEAR TRANSFORMATIONS WHICH MAP THE CLASS OF INVERSE M-MATRICES ONTO ITSELF
Main Article Content
Abstract
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).
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
A. Berman, D. Hershkowitz and C. R. Johnson, "Linear transformations that preserve certain positivity classes of matrices," Linear Algebra Appl. 68: 9-29 (1985).
A. Berman and 0. Kessler, "Matrices with a transitive graph and inverse M-matrices," Linear Algebra. Appl. 71: 175-185 (1985).
A. Berman and R. J. Plemmons, Nonnegative Matrice in the Mathematical Science, Academic Press, New York, 1979.
M. Fiedler, C. R. Johnson and T. L. Markham, "Notes on inverse M-matrices," Linear Algebra Appl. 91: 75-81 (1987}.
M. Fiedler and T. L. Markham, "A characterization of the closure of inverse M-matrices," Linear Algebra Appl. 105: 209-223 (198S},
S. Friedland, D. Hershkowitz and H. Schneider, "Matrices whose powers are M-matrices or Z- matrices," Trana. Amer. Math. Soc. 300: 343-366 (1987).
D. Hershkowitz and C. R . Johnson, "Linear transformations that map the P-matrices into themselves," Linea.r Algebra Appl. 74: 23-38 (1986).
C. R . Johnson, "Inverse M-matrices," Linear Algebra Appl. 47: 195-216 (1982).
C. R. Johnson, "Closure properties of certain positivity classes of matrices under various algebraic operations," Linear Algebra Appl. 97: 243-247 (1987).
M. Lewin and M. Neumann, "On the inverse M-matrix problem for (0,1)-matrices," Linear Algebra Appl. 30: 41-50 (1980),