We give a counterexample to a conjecture about the possible Jordan normal forms of nilpotent matrices where the entries in the upper triangular part are prescribed. 0 Elsevier Science Inc., 1997 Let A = [ai,j] be an n X n matrix where the entries ai, j, with i <j, are fixed constants, all the other
On the jordan form of completions of partial upper triangular matrices
✍ Scribed by C. Jordán; J.R. Torregrosa; A. Urbano
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 520 KB
- Volume
- 254
- Category
- Article
- ISSN
- 0024-3795
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✦ Synopsis
two completion conjectures for partial upper triangular matrices. In this paper we show that one of them is not true in general, and we prove its validity for some particular cases. We also prove the equivalence between the two conjectures in the case of partial Hessenherg matrices.
📜 SIMILAR VOLUMES
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