LINEAR TRANSFORMATIONS WHICH MAP THE CLASS OF INVERSE M-MATRICES ONTO ITSELF

Authors

  • BIT-SHUN TAM Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, Republic of China.
  • PO-HONG LIOU Department of Mathematics, Tamkang University, Tamsui, Taiwan 25137, Republic of China.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4651

Keywords:

linear preservers, linear transformations, inverse M-matrices

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).

References

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A. Berman and R. J. Plemmons, Nonnegative Matrice in the Mathematical Science, Academic Press, New York, 1979.

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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).

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M. Lewin and M. Neumann, "On the inverse M-matrix problem for (0,1)-matrices," Linear Algebra Appl. 30: 41-50 (1980),

Published

1990-06-01

How to Cite

TAM, B.-S., & LIOU, P.-H. (1990). LINEAR TRANSFORMATIONS WHICH MAP THE CLASS OF INVERSE M-MATRICES ONTO ITSELF. Tamkang Journal of Mathematics, 21(2), 159–167. https://doi.org/10.5556/j.tkjm.21.1990.4651

Issue

Section

Papers