LINEAR PRESERVERS OF BOOLEAN NILPOTENT MATRICES

Title & Authors
LINEAR PRESERVERS OF BOOLEAN NILPOTENT MATRICES
Song, Seok-Zun; Kang, Kyung-Tae; Jun, Young-Bae;

Abstract
For an $\small{n{\times}n}$ Boolean matrix A, A is called nilpotent if $\small{A^m=O}$ for some positive integer m. We consider the set of $\small{n{\times}n}$ nilpotent Boolean matrices and we characterize linear operators that strongly preserve nilpotent matrices over Boolean algebras.
Keywords
Boolean algebra;nilpotent matrix;constituent;linear operator;
Language
English
Cited by
1.
선형보존자 문제들에 관한 연구,송석준;

대한수학회논문집, 2006. vol.21. 4, pp.595-612
1.
Primitive symmetric matrices and their preservers, Linear and Multilinear Algebra, 2017, 65, 1, 129
2.
Regular matrices and their strong preservers over semirings, Linear Algebra and its Applications, 2008, 429, 1, 209
3.
On linear operators strongly preserving invariants of Boolean matrices, Czechoslovak Mathematical Journal, 2012, 62, 1, 169
4.
Zero-term rank and zero-star cover number of symmetric matrices and their linear preservers, Linear and Multilinear Algebra, 2016, 64, 12, 2368
5.
The Invertible Linear Operator Preserving {1,2}-Inverses of Matrices over Semirings, Pure Mathematics, 2015, 05, 01, 8
References
1.
L. B. Beasley and N. J. Pullman, Boolean rank preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77

2.
L. B. Beasley and N. J. Pullman, Operators that preserve semiring matrix functions, Linear Algebra Appl. 99 (1988), 199-216

3.
P. Botta, S. Pierce, and W. Watkins, Linear transformations that preserve the nilpotent matrices, Pacific J. Math. 104 (1983), no. 1, 39-46

4.
K. H. Kim, Boolean matrix theory and applications, Pure and Applied Mathemat ics, Vol. 70, Marcel Dekker, New York, 1982

5.
S. Kirkland and N. J. Pullman, Linear operators preserving invariants of non- binary matrices, Linear Multilinear Algebra 33 (1993), 295-300

6.
S. -Z. Song, L. B. Beasley, G. -S. Cheon, and Y. -B. Jun, Rank and perimeter preservers of Boolean rank-1 matrices, J. Korean Math. Soc. 41 (2004), no. 2, 397-406

7.
S. -Z. Song and S. -G. Lee, Column ranks and their preservers of general Boolean matrices, J. Korean Math. Soc. 32 (1995), no. 3, 531-540