Multivariate Hasse–Schmidt derivation on exterior algebras

ABSTRACT

The purpose of this short note is to consider multivariate Hasse-Schmidt derivations on exterior algebras and to show how they easily provide remarkable identities, holding in the algebra of square matrices, which generalize the classical theorem of Cayley–Hamilton.

Keywords:

• Hasse–Schmidt derivation on exterior algebra
• traces of ordered tuples of endomorphisms
• generalized Cayley–Hamilton theorem
• exterior algebra

2010 Mathematics Subject Classification:

• 15A75

Acknowledgments

Warm words of gratitude are due to the Referee. Her/his patient and carefully reading of the first versions of the manuscript helped me to greatly improve the exposition.

Disclosure statement

No potential conflict of interest was reported by the authors.