The trace formulas yield the inverse metric formula

Details The trace formulas yield the inverse metric formula The trace formulas yield the inverse metric formula

1998-05-06

arxiv.org/abs/math-ph/9805006v4

J. Math. Phys. 39 (1998) 6206-6213

Physics

Mathematical Physics

11 pages, no figures, LaTeX. The title has been changed in this new version

Scientific paper

It is a well-known fact that the first and last non-trivial coefficients of the characteristic polynomial of a linear operator are respectively its trace and its determinant. This work shows how to compute recursively all the coefficients as polynomial functions in the traces of successive powers of the operator. With the aid of Cayley-Hamilton's theorem the trace formulas provide a rational formula for the resolvent kernel and an operator-valued null identity for each finite dimension of the underlying vector space. The 4-dimensional resolvent formula allows an algebraic solution of the inverse metric problem in general relativity.

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