Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Factor Rank and Its Preservers of Integer Matrices

  • Received : 2005.09.02
  • Published : 2006.12.23
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Abstract

We characterize the linear operators which preserve the factor rank of integer matrices. That is, if $\mathcal{M}$ is the set of all $m{\times}n$ matrices with entries in the integers and min($m,n$) > 1, then a linear operator T on $\mathcal{M}$ preserves the factor rank of all matrices in $\mathcal{M}$ if and only if T has the form either T(X) = UXV for all $X{\in}\mathcal{M}$, or $m=n$ and T(X)=$UX^tV$ for all $X{\in}\mathcal{M}$, where U and V are suitable nonsingular integer matrices. Other characterizations of factor rank-preservers of integer matrices are also given.

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References

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