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Diagonability of idempotent matrices over noncommutative rings

✍ Scribed by Guangtian Song; Xuejun Guo

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
83 KB
Volume
297
Category
Article
ISSN
0024-3795

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✦ Synopsis

Let R be an arbitrary ring. In this paper, the following statements are proved: (a) Each idempotent matrix over R can be diagonalized if and only if each idempotent matrix over R has a characteristic vector. (b) An idempotent matrix over R can be diagonalized under a similarity transformation if and only if it is equivalent to a diagonal matrix. (a) and (b) generalize Foster's and Steger's theorems to arbitrary rings. We give some new results about 0-similarity of idempotent matrices over R.

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