Song, Seok-Zun Linear operators that preserve column rank of Boolean matrices. (English) Zbl 0802.15006 Proc. Am. Math. Soc. 119, No. 4, 1085-1088 (1993). Let \(T\) be a linear transformation of the matrix algebra (of order \(\geq 4)\) over a Boolean algebra. The main result shows that \(T\) preserves the column rank if and only if there are invertible matrices \(U\) and \(V\) such that \(T(A) = UAV\) for all \(A\). Reviewer: J.Zemánek (Warszawa) Cited in 5 Documents MSC: 15A30 Algebraic systems of matrices 15A03 Vector spaces, linear dependence, rank, lineability 15A04 Linear transformations, semilinear transformations Keywords:rank preserving operator; linear transformation; matrix algebra; Boolean algebra PDFBibTeX XMLCite \textit{S.-Z. Song}, Proc. Am. Math. Soc. 119, No. 4, 1085--1088 (1993; Zbl 0802.15006) Full Text: DOI References: [1] LeRoy B. Beasley and Seok-Zun Song, A comparison of nonnegative real ranks and their preservers, Linear and Multilinear Algebra 31 (1992), no. 1-4, 37 – 46. · Zbl 0781.15006 · doi:10.1080/03081089208818120 [2] LeRoy B. Beasley and Norman J. Pullman, Semiring rank versus column rank, Linear Algebra Appl. 101 (1988), 33 – 48. · Zbl 0642.15002 · doi:10.1016/0024-3795(88)90141-3 [3] LeRoy B. Beasley and Norman J. Pullman, Boolean-rank-preserving operators and Boolean-rank-1 spaces, Linear Algebra Appl. 59 (1984), 55 – 77. · Zbl 0536.20044 · doi:10.1016/0024-3795(84)90158-7 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.