TITLE:
Tropical (0, −1) Idempotent Matrix
AUTHORS:
Chonghua Cheng, Dandan Su
KEYWORDS:
Tropical Algebra, Idempotent Matrix, Binary Boolean Semirings
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.4,
April
16,
2026
ABSTRACT: For an
n×n
tropical
(
0,−1
)
matrix
A
, we first give the necessary and sufficient conditions for
A
to be an idempotent matrix when the diagonal elements of
A
are all 0 and all −1, respectively. Then we give some necessary conditions for some special tropical
(
0,−1
)
matrices to be idempotent matrices. Finally, we discuss the relationship between the matrix set
M
n
(
T
)
under the tropical
(
0,−1
)
semiring and the matrix set
M
n
(
ℬ
)
under the binary Boolean semiring
ℬ
.