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J. Korean Math. Soc. 2008; 45(4): 1043-1056
Printed July 1, 2008
Copyright © The Korean Mathematical Society.
Linear preservers of spanning column rank of matrix products over semirings
Seok-Zun Song, Gi-Sang Cheon, and Young-Bae Jun
Cheju National University, Sungkyunkwan University, Gyeongsang National University
The spanning column rank of an $m \times n$ matrix $A$ over a semiring is the minimal number of columns that span all columns of $A$. We characterize linear operators that preserve the sets of matrix ordered pairs which satisfy multiplicative properties with respect to spanning column rank of matrices over semirings.
Keywords: antinegative semiring, spanning column rank, $(P,Q,B)$-operator, rank inequality
MSC numbers: 15A03, 15A04, 15A45
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