A simplified version of the Cayley-Hamilton theorem and exponential forms of the 2 × 2 and 3 × 3 matrices

G. Dattoli, C. Mari, A. Torre

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Abstract

In this note we present a simple proof of a theorem allowing us to cast f(Â), where  is a non-singular matrix and f a function admitting a McLaurin expansion, as a finite sum. We also discuss the complementary version of the theorem and, limiting ourselves to 2 × 2 and 3×3 matrices, we show how they can be cast in an exponential form. Such form greatly simplifies the task of finding the π-th power (with π being any real or complex number) of a given matrix. The applications to physical problems like the optical-resonator stability and the Cabibbo-Kobayashi-Maskawa matrix are also discussed. © 1993 Società Italiana di Fisica.
Original languageEnglish
Pages (from-to)61 - 68
Number of pages8
JournalNuovo Cimento della Societa Italiana di Fisica B
Volume108
Issue number1
DOIs
Publication statusPublished - Jan 1993
Externally publishedYes

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

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