In this paper we prove that, up to a scalar multiple, the determinant is the unique generalized matrix function that preserves the product or remains invariant under similarity. Also, we present a new proof for the known result that, up to a scalar multiple, the ordinary characteristic polynomial is the unique generalized characteristic polynomial for which the Cayley-Hamilton theorem remains true.
@article{bwmeta1.element.doi-10_2478_s11533-013-0347-0,
author = {Mohammad Jafari and Ali Madadi},
title = {Generalized matrix functions and determinants},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {464-469},
zbl = {1297.15008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0347-0}
}
Mohammad Jafari; Ali Madadi. Generalized matrix functions and determinants. Open Mathematics, Tome 12 (2014) pp. 464-469. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0347-0/
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