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Characterization
of Rank of a
Matrix Over the
Symmetrized
Max-Plus Algebra
Suroto (1), Diah Junia Eksi Palupi (2)
and Ari
Suparwanto
(3)
(1) Department
of Mathematics,
Universitas
Jenderal
Soedirman,
Purwokerto,
Central Java,
Indonesia
Email address:
suroto@unsoed.ac.id
(2) Department of
Mathematics,
Universitas Gadjah
Mada, Yogyakarta,
Indonesia
Email address:
diah yunia@ugm.ac.id
(3) Department of
Mathematics,
Universitas Gadjah
Mada, Yogyakarta,
Indonesia
Email address:
ari_suparwanto@ugm.ac.id
Doi :
https://doi.org/10.47013/15.4.4
Cited by :
Jordan J. Math &
Stat.,
15 (4A) (2022),
843 - 856
PDF
Received on:
April 16,
2021;
Accepted
on: Feb. 27,
2022
Abstract. In this
paper, we
characterize the
rank of a matrix
over the
symmetrized
max-plus
algebra. This
characterization
is based on
linearly
independence of
columns or rows
of the matrix in
balance sense.
We show that the
rank of such a
matrix can be
determined using
maximum number
of rows or
columns which
are linearly
independent in
balance sense.
This completes
the discussion
in [1] which
only uses minors
to determine
rank of matrix.
Keywords: Characterization,
Rank, Linear
Independent,
Symmetrized
Max-Plus
Algebra.
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