M₂-rank differences for overpartitions
Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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Jeremy Lovejoy, Robert Osburn (2010)
Acta Arithmetica
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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.
A. Lachlan (1974)
Fundamenta Mathematicae
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Irina Gelbukh (2015)
Czechoslovak Mathematical Journal
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For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number...
G. S. Rogers (1983)
Applicationes Mathematicae
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Robin Harte (1995)
Studia Mathematica
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Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.
Beasley, LeRoy B. (1999)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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A. Lachlan (1980)
Fundamenta 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.
Matej Brešar, Peter Šemrl (1998)
Studia Mathematica
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Let A be a semisimple Banach algebra. We define the rank of a nonzero element a in the socle of A to be the minimum of the number of minimal left ideals whose sum contains a. Several characterizations of rank are proved.
Charles H. Kraft, Constance Van Eeden (1969-1970)
Publications mathématiques et informatique de Rennes
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