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 “The three point pick problem on the bidisk.”
The maximal and minimal ranks of with applications.
Minimum rank of matrices described by a graph or pattern over the rational, real and complex numbers.
Berman, Avi, Friedland, Shmuel, Hogben, Leslie, Rothblum, Uriel G., Shader, Bryan (2008)
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.
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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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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Fermat's theorem for matrices revisited
Štefan Schwarz (1985)
Mathematica Slovaca
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A complete characterization of invariant jointly rank- convex quadratic forms and applications to composite materials
Vincenzo Nesi, Enrico Rogora (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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The theory of compensated compactness of Murat and Tartar links the algebraic condition of rank- convexity with the analytic condition of weak lower semicontinuity. The former is an algebraic condition and therefore it is, in principle, very easy to use. However, in applications of this theory, the need for an efficient classification of rank- convex forms arises. In the present paper, we define the concept of extremal -forms and characterize them in the rotationally invariant...
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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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.