논문KCI 등재
Factor Rank and Its Preservers of Integer Matrices
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Abstract
We characterize the linear operators which preserve the factor rank of integer matrices. That is, if M is the set of all m £ n matrices with entries in the integers and min(m; n) > 1, then a linear operator T on M preserves the factor rank of all matrices in M if and only if T has the form either T(X) = UXV for all X 2 M, or m = n and T(X) = UXtV for all X 2M, where U and V are suitable nonsingular integer matrices. Other characterizations of factor rank-preservers of integer matrices are also given.
참고문헌 (7)
- "Linear preservers ofzeros of matrix polynomials", 401, pp.325~340 (2005)
- "Column ranks and theirpreservers over nonnegative real matrices", 399, pp.3~16 (2005)
- "Linear transformations on matrices", pp.343~345 (1981)
- "Linear transformations on algebras of matrices", 11, pp.61~66 (1959)
- "Transformations on tensor product spaces", 9, pp.1215~1221 (1959)
- "Linear operators that preserve maximal column ranks of nonnegative integermatrices", 126, pp.2205~2211 (1998)
- "Perimeter preservers of nonnegative integer matrices", 45, pp.9~15 (2004)
관련 논문AI추천
Maximal column rank preservers of integer matrices강경태, 송석준대한수학회 · 대한수학회논문집2007 · 제22권 제2호Rank-preserving operators of nonnegative integer matrices강경태, 송석준, 전영배대한수학회 · 대한수학회논문집2005 · 제20권 제4호Factor Rank Comparisons of Matrices over Two Related Semirings송석준대한수학회 · 대한수학회논문집2006 · 제21권 제2호Maximal column ranks and their preservers of Matrices Over Max Algebra강경태, 송석준대한수학회 · 대한수학회지2003 · 제40권 제6호Sets of Integer Matrix Pairs Derived from Row Rank Inequalities and Their Preservers송석준, 전영배경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2013 · 제53권 제2호Commuting Pair Preservers of MatricesJin-Young Oh, Seok-Zun Song경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제2호
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