On the partial ordering of almost definite matrices
Ar. Meenakshi (1989)
Czechoslovak Mathematical Journal
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Displaying similar documents to “Remarks on inertia theorems for matrices”
On the partial ordering of almost definite matrices
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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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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Preservers of the rank of matrices over a field.
Kalinowski, Józef (2009)
Beiträge zur Algebra und Geometrie
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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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The rank of the difference of similar matrices
Marques de Sá, Eduardo (1989)
Portugaliae mathematica
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On the Yang-Baxter-like matrix equation for rank-two matrices
Duanmei Zhou, Guoliang Chen, Jiu Ding (2017)
Open Mathematics
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Let A = PQT, where P and Q are two n × 2 complex matrices of full column rank such that QTP is singular. We solve the quadratic matrix equation AXA = XAX. Together with a previous paper devoted to the case that QTP is nonsingular, we have completely solved the matrix equation with any given matrix A of rank-two.