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On a conjecture about the Jordan form of completions of partial upper triangular matrices

✍ Scribed by Fernando C. Silva

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
144 KB
Volume
260
Category
Article
ISSN
0024-3795

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✦ Synopsis

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 entries are distinct variables, and trace A = 0. A completion of A is any matrix that can be obtained from A by replacing the variables by arbitrary constants. Let %? be the set of all the completions of A.

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