Linear maps preserving rank 2 on the space of alternate matrices and their applications.
Cao, Chongguang, Tang, Xiaomin (2004)
International Journal of Mathematics and Mathematical Sciences
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Displaying similar documents to “Densities for certain -ranks in cyclic fields of degree ”
Linear maps preserving rank 2 on the space of alternate matrices and their applications.
Zero-term rank preservers of integer matrices
Seok-Zun Song, Young-Bae Jun (2006)
Discussiones Mathematicae - General Algebra and Applications
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The zero-term rank of a matrix is the minimum number of lines (row or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve the zero-term rank of the m × n integer matrices. That is, a linear operator T preserves the zero-term rank if and only if it has the form T(A)=P(A ∘ B)Q, where P, Q are permutation matrices and A ∘ B is the Schur product with B whose entries are all nonzero integers.
Fermat's theorem for matrices revisited
Štefan Schwarz (1985)
Mathematica Slovaca
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Matrix field extensions
Jacob Beard, Robert Mcconnel (1982)
Acta Arithmetica
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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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A basic decomposition result related to the notion of the rank of a matrix and applications.
Mortici, Cristinel (2003)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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On 3-class groups of non-Galois cubic fields
Kiyoaki Iimura (1979)
Acta Arithmetica
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Perimeter preserver of matrices over semifields
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.