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http://hdl.handle.net/1942/16076| Title: | The nullity theorem for principal pivot transform | Authors: | BRIJDER, Robert | Issue Date: | 2013 | Source: | LINEAR ALGEBRA AND ITS APPLICATIONS, 439 (11), p. 3638-3642 | Abstract: | We generalize the nullity theorem of Gustafson (1984) [8] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation on graphs. As an application, we show that a particular matrix polynomial, the so-called nullity polynomial, is invariant under principal pivot transform. (C) 2013 Elsevier Inc. All rights reserved. | Notes: | Brijder, R (reprint author), Hasselt Univ, Diepenbeek, Belgium. robert.brijder@uhasselt.be | Keywords: | Nullity theorem; Principal pivot transform; Schur complement; Local complementation; Nullity polynomial | Document URI: | http://hdl.handle.net/1942/16076 | ISSN: | 0024-3795 | e-ISSN: | 1873-1856 | DOI: | 10.1016/j.laa.2013.09.014 | ISI #: | 000327174000025 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
| Appears in Collections: | Research publications |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| brijder 1.pdf | Published version | 163.47 kB | Adobe PDF | View/Open |
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