A new Cayley-Hamilton theorem. (English) Zbl 0972.15004

Kennedy, Stephen; Stafford, Matthew; Williams, R. F.

Uhlenbeck, Karen (ed.), Global analysis in modern mathematics. Proceedings of the symposium in honor of Richard Palais’ sixtieth birthday, University of Maine, Orono, ME, USA, August 8-10, 1991, and at Brandeis University, Waltham, MA, USA, August 12, 1992. Houston, TX: Publish or Perish, Inc. 247-251 (1993).

The authors show that, for the characteristic polynomial \(\chi\) based on a non-Abelian determinant the Cayley-Hamilton theorem holds, that is \(\chi_A(A)\) is always zero.
For the entire collection see [Zbl 0920.00058].

Reviewer: Messoud Efendiev (Berlin)

MSC:

15A24	Matrix equations and identities
15A15	Determinants, permanents, traces, other special matrix functions
15A18	Eigenvalues, singular values, and eigenvectors

Keywords:

matrix identity; characteristic polynomial; non-Abelian determinants; Cayley-Hamilton theorem