Zero-nonzero patterns for nilpotent matrices over finite fields.

Vander Meulen, Kevin N.; Van Tuyl, Adam

Displaying similar documents to “Zero-nonzero patterns for nilpotent matrices over finite fields.”

Generating potentially nilpotent full sign patterns.

Kim, In-Jae, Olesky, Dale D., Shader, Bryan L., Van Den Driessche, Pauline, Van Der Holst, Hein, Vander Meulen, Kevin N. (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Nilpotent matrices and spectrally arbitrary sign patterns.

Pereira, Rajesh (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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On determining minimal spectrally arbitrary patterns.

Cavers, Michael S., Kim, In Jae, Shader, Bryan L., Vander Meulen, Kevin N. (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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Products of commuting nilpotent operators.

Kokol Bukovšek, Damjana, Košir, Tomaž, Novak, Nika, Oblak, Polona (2007)

ELA. The Electronic Journal of Linear Algebra [electronic only]

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On potentially nilpotent double star sign patterns

Honghai Li, Jiongsheng Li (2009)

Czechoslovak Mathematical Journal

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A matrix $𝒜$ whose entries come from the set ${+, -, 0}$ is called a , or . A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, the characterization problem for some potentially nilpotent double star sign patterns is discussed. A class of double star sign patterns, denoted by $𝒟 S S P (m, 2)$ , is introduced. We determine all potentially nilpotent sign patterns in $𝒟 S S P (3, 2)$ and $𝒟 S S P (5, 2)$ , and prove that one sign pattern in $𝒟 S S P (3, 2)$ is potentially stable.

Computer search for nilpotent complexes.

Lewis, Robert H., Moore, Guy D. (1997)

Experimental Mathematics

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On Kolchin's theorem.

Israel N. Herstein (1986)

Revista Matemática Iberoamericana

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A well-known theorem due to Kolchin states that a semi-group G of unipotent matrices over a field F can be brought to a triangular form over the field F [4, Theorem H]. Recall that a matrix A is called unipotent if its only eigenvalue is 1, or, equivalently, if the matrix I - A is nilpotent. Many years ago I noticed that this result of Kolchin is an immediate consequence of a too-little known result due to Wedderburn [6]. This result of Wedderburn asserts that if B is a finite...