Variation in Jordan structure under congruence: the nonsingular case

• Type: Article in International Scientific Journal
• Date: 2009

Authors

Susana Borges Furtado (Author) FEP; Charles Johnson (Author) Other

Journal

Title: LINEAR & MULTILINEAR ALGEBRA

Vol. 57 No. 1

Pages: 29-54

ISSN: 0308-1087

Indexing

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Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-003-R74

DOI: 10.1080/03081080701553719

Abstract (EN): In earlier work, the possible spectra in a congruence class and the possible Jordan forms, among nilpotent matrices congruent to a given nilpotent matrix, were characterized. Here, we study the natural, but quite different, question of possible Jordan forms of matrices with a single nonzero eigenvalue (which may be taken to be 1) that are congruent to a given matrix with that eigenvalue. We focus upon a class of matrices that includes the essentially real matrices for which 0 is not in the field of values. Unlike the nilpotent case, the number of Jordan blocks, as well as their sizes, may change. Necessary conditions are derived and then it is shown that they are sufficient through a lengthy construction process. Some of the results go beyond the indicated case, but do not cover general matrices.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 26