Rank and perimeter preserver of rank-1 matrices over max algebra

• Autorzy: Seok-Zun Song , Kyung-Tae Kang
• Języki publikacji: EN

Abstrakty

EN

For a rank-1 matrix $A = a ⊗ b^{t}$ over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or $T(A) = U ⊗ A^{t} ⊗ V$ with some monomial matrices U and V.

Słowa kluczowe

EN

max algebra; semiring; linear operator; monomial; rank; dominate; perimeter; (U,V)-operator

Kategorie tematyczne

• 16Y60: Semirings
• 15A04: Linear transformations, semilinear transformations
• 15A03: Vector spaces, linear dependence, rank
• 12K10: Semifields

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2003
• Tom: 23
• Numer: 2
• Strony: 125-137

Daty

wydano

2003

otrzymano

2003-04-24

Twórcy

autor

Seok-Zun Song

• Department of Mathematics, Cheju National University, Jeju 690-756, Republic of Korea

autor

Kyung-Tae Kang

• Department of Mathematics, Cheju National University, Jeju 690-756, Republic of Korea

Bibliografia

• [1] R.B. Bapat, A max version of the Perron-Frebenius theorem, Linear Algebra Appl. 275-276 (1998), 3-18.
• [2] R.B. Bapat, S. Pati and S.-Z. Song, Rank preservers of matrices over max algebra, Linear and Multilinear Algebra 48 (2000), 149-164.
• [3] L.B. Beasley and N.J. Pullman, Boolean rank-preserving operators and Boolean rank-1 spaces, Linear Algebra Appl. 59 (1984), 55-77.
• [4] L.B. Beasley, S.-Z. Song and S.-G. Lee, Zero term rank preservers, Linear and Multilinear Algebra 48 (2001), 313-318.
• [5] S.-Z. Song and S.-R. Park, Maximal column rank preservers of fuzzy matrices, Discuss. Math. - Gen. Algebra Appl. 21 (2001), 207-218.

Identyfikatory

DOI

10.7151/dmgaa.1068