Spaces of rank-2 matrices over GF(2).
Beasley, LeRoy B. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Beasley, LeRoy B. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Cao, Chongguang, Tang, Xiaomin (2004)
International Journal of Mathematics and Mathematical Sciences
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Štefan Schwarz (1985)
Mathematica Slovaca
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Yong Ge Tian, George P. H. Styan (2002)
Commentationes Mathematicae Universitatis Carolinae
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It is shown that where is idempotent, has full row rank and . Some applications of the rank formula to generalized inverses of matrices are also presented.
Kalinowski, Józef (2009)
Beiträge zur Algebra und Geometrie
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Pedregal, Pablo, Šverák, Vladimír (1998)
Journal of Convex Analysis
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Seok-Zun Song, Kyung-Tae Kang, Young Bae Jun (2006)
Czechoslovak Mathematical Journal
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For a rank- matrix , we define the perimeter of as the number of nonzero entries in both and . We characterize the linear operators which preserve the rank and perimeter of rank- matrices over semifields. That is, a linear operator preserves the rank and perimeter of rank- matrices over semifields if and only if it has the form , or with some invertible matrices U and V.
Seok-Zun Song, Kyung-Tae Kang, Sucheol Yi (2004)
Commentationes Mathematicae Universitatis Carolinae
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We investigate the perimeter of nonnegative integer matrices. We also characterize the linear operators which preserve the rank and perimeter of nonnegative integer matrices. That is, a linear operator preserves the rank and perimeter of rank- matrices if and only if it has the form , or with appropriate permutation matrices and and positive integer matrix , where denotes Hadamard product.