# Generalized matrix functions and determinants

Open Mathematics (2014)

- Volume: 12, Issue: 3, page 464-469
- ISSN: 2391-5455

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topMohammad Jafari, and Ali Madadi. "Generalized matrix functions and determinants." Open Mathematics 12.3 (2014): 464-469. <http://eudml.org/doc/269384>.

@article{MohammadJafari2014,

abstract = {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.},

author = {Mohammad Jafari, Ali Madadi},

journal = {Open Mathematics},

keywords = {Generalized matrix functions; Determinants; Generalized characteristic polynomials; determinant; generalized matrix function; characteristic polynomial; Cayley-Hamilton theorem},

language = {eng},

number = {3},

pages = {464-469},

title = {Generalized matrix functions and determinants},

url = {http://eudml.org/doc/269384},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Mohammad Jafari

AU - Ali Madadi

TI - Generalized matrix functions and determinants

JO - Open Mathematics

PY - 2014

VL - 12

IS - 3

SP - 464

EP - 469

AB - 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.

LA - eng

KW - Generalized matrix functions; Determinants; Generalized characteristic polynomials; determinant; generalized matrix function; characteristic polynomial; Cayley-Hamilton theorem

UR - http://eudml.org/doc/269384

ER -

## References

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- [2] Darafsheh M.R., Mallahi K., Pournaki M.R., A note on Cayley-Hamilton theorem for generalized matrix function, Pure Math. Appl., 2000, 11(4), 553–557 Zbl0994.15032
- [3] Jafari M.H., Madadi A.R., On the equality of generalized matrix functions, Linear Algebra Appl. (in press), DOI: 10.1016/j.laa.2012.04.027 [Crossref] Zbl1293.15004
- [4] Marcus M., Finite Dimensional Multilinear Algebra, I, Pure Appl. Math., 23, Marcel Dekker, New York, 1973
- [5] Merris R., Generalized matrix functions: a research problem, Linear and Multilinear Algebra, 1979/80, 8(1), 83–86 http://dx.doi.org/10.1080/03081087908817302[Crossref]
- [6] Merris R., Multilinear Algebra, Algebra Logic Appl., 8, Gordon and Breach, Amsterdam, 1997
- [7] Zhang F., Matrix Theory, 2nd ed., Universitext, Springer, New York, 2011 http://dx.doi.org/10.1007/978-1-4614-1099-7[Crossref]

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