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Drazin invertibility for matrices over an arbitrary ring

✍ Scribed by R. Puystjens; M.C. Gouveia

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
190 KB
Volume
385
Category
Article
ISSN
0024-3795

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✦ Synopsis

Characterizations are given for existence of the Drazin inverse of a matrix over an arbitrary ring. Moreover, the Drazin inverse of a product P AQ for which there exist a P and Q such that P P A = A = AQQ can be characterized and computed. This generalizes recent results obtained for the group inverse of such products.

The results also apply to morphisms in (additive) categories.

As an application we characterize Drazin invertibility of companion matrices over general rings.

πŸ“œ SIMILAR VOLUMES

Orthogonality Matrices for Modules over
Orthogonality Matrices for Modules over Finite Frobenius Rings and MacWilliams' Equivalence Theorem
✍ Marcus Greferath πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 106 KB

MacWilliams' equivalence theorem states that Hamming isometries between linear codes extend to monomial transformations of the ambient space. One of the most elegant proofs for this result is due to K. P. Bogart et al. (1978, Inform. and Control 37, 19-22) where the invertibility of orthogonality ma