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On the structure of commutative matrices. II

✍ Scribed by Tomaž Košir


Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
731 KB
Volume
261
Category
Article
ISSN
0024-3795

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✦ Synopsis


The theorem (due to Suprunenko and Tyshkevich) that the algebra LZ' generated by A and the identity matrix has dimension equal to N is proved. A canonical basis for & is given, and related structure constants are discussed.


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On the irreducibility of commuting varie
✍ Roberta Basili 📂 Article 📅 2003 🏛 Elsevier Science 🌐 English ⚖ 321 KB

Given an n × n nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the n × n nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the pairs (A, B) of n × n nilpotent matrices over K such that [