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Normal forms of generic triangular band matrices and Jordan forms of nilpotent completions

✍ Scribed by MichaelI. Gekhtman; Leiba Rodman

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
195 KB
Volume
308
Category
Article
ISSN
0024-3795

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✦ Synopsis

Sets of possible Jordan forms of nilpotent matrices with a given upper triangular part are studied. It is proved that, for generic matrices within a set of triangular band matrices, the set of Jordan forms contains a unique minimal (in the sense of majorization) Jordan form. Moreover, in the generic case, there exists a nilpotent matrix in the orbit of a given upper triangular matrix having the minimal Jordan form, and also having the minimal rank among all matrices with the given upper triangular part. The orbit is understood in the sense of the triangular group action. Normal, or canonical, forms of the triangular group action (again, in the generic case) serve as the main technical tool in proving these results. The normal forms are also independently interesting, and are used to study triangular equivalence.

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