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

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.

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...