The maximal and minimal ranks of with applications.
Tian, Yongge, Cheng, Shizhen (2003)
The New York Journal of Mathematics [electronic only]
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Displaying similar documents to “Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.”
The maximal and minimal ranks of with applications.
On the function “sandwiched" between and .
Dobrynin, V.Y. (1997)
The Electronic Journal of Combinatorics [electronic only]
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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.
Universally optimal matrices and field independence of the minimum rank of a graph.
Dealba, Luz M., Grout, Jason, Hogben, Leslie, Mikkelson, Rana, Rasmussen, Kaela (2009)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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The rank of a cograph.
Royle, Gordon F. (2003)
The Electronic Journal of Combinatorics [electronic only]
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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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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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Minimum rank of a tree over an arbitrary field.
Chenette, Nathan L., Droms, Sean V., Hogben, Leslie, Mikkelson, Rana, Pryporova, Olga (2007)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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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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Low rank co-diagonal matrices and Ramsey graphs.
Grolmusz, Vince (2000)
The Electronic Journal of Combinatorics [electronic only]
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A note on minimum rank and maximum nullity of sign patterns.
Hogben, Leslie (2011)
ELA. The Electronic Journal of Linear Algebra [electronic only]
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A new rank formula for idempotent matrices with applications
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.