Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

Details Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity Trace Formulae of Characteristic Polynomial and Cayley-Hamilton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity

2007-01-12

arxiv.org/abs/hep-th/0701116v1

Commun.Theor.Phys.49:801,2008

Physics

High Energy Physics

High Energy Physics - Theory

10 pages

Scientific paper

10.1088/0253-6102/49/4/01

By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and then we obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given, and which implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to chiral perturbation theory and general relativity.

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