Weak convergence of linear rank statistics
Béla Gyires (1980)
Banach Center Publications
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Béla Gyires (1980)
Banach Center Publications
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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.
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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G. S. Rogers (1983)
Applicationes Mathematicae
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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.
Bose, Arup, Sen, Arnab (2007)
Electronic Communications in Probability [electronic only]
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Beasley, LeRoy B. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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Dana Vorlíčková (1991)
Kybernetika
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