Abstract
This note presents a simple proof of a theorem allowing to cast f (A-tilde), where A-tilde is a non singular matrix and f a function admitting a McLaurin expansion, as a finite sum. The note also discusses the complementary version of the theorem and limits the discussion to 2x2 and 3x3 matrices. It is shown how they can be cast in an exponential form. Such a form greatly simplifies the task of finding the u/sup th/ power (with u 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 dealt with.
Citation Formats
Dattoli, G, Mari, C, and Torre, A.
Simplified version of Cayley Hamilton theorem and exponential forms of 2 x 2 and 3 x 3 matrices.
Italy: N. p.,
1992.
Web.
Dattoli, G, Mari, C, & Torre, A.
Simplified version of Cayley Hamilton theorem and exponential forms of 2 x 2 and 3 x 3 matrices.
Italy.
Dattoli, G, Mari, C, and Torre, A.
1992.
"Simplified version of Cayley Hamilton theorem and exponential forms of 2 x 2 and 3 x 3 matrices."
Italy.
@misc{etde_10147222,
title = {Simplified version of Cayley Hamilton theorem and exponential forms of 2 x 2 and 3 x 3 matrices}
author = {Dattoli, G, Mari, C, and Torre, A}
abstractNote = {This note presents a simple proof of a theorem allowing to cast f (A-tilde), where A-tilde is a non singular matrix and f a function admitting a McLaurin expansion, as a finite sum. The note also discusses the complementary version of the theorem and limits the discussion to 2x2 and 3x3 matrices. It is shown how they can be cast in an exponential form. Such a form greatly simplifies the task of finding the u/sup th/ power (with u 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 dealt with.}
place = {Italy}
year = {1992}
month = {Feb}
}
title = {Simplified version of Cayley Hamilton theorem and exponential forms of 2 x 2 and 3 x 3 matrices}
author = {Dattoli, G, Mari, C, and Torre, A}
abstractNote = {This note presents a simple proof of a theorem allowing to cast f (A-tilde), where A-tilde is a non singular matrix and f a function admitting a McLaurin expansion, as a finite sum. The note also discusses the complementary version of the theorem and limits the discussion to 2x2 and 3x3 matrices. It is shown how they can be cast in an exponential form. Such a form greatly simplifies the task of finding the u/sup th/ power (with u 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 dealt with.}
place = {Italy}
year = {1992}
month = {Feb}
}