%0 Journal Article %1 silva98 %A Silva, Ronaldo Rodrigues %D 1998 %J Journal of Mathematical Physics %K characteristic eigenvalues linear.algebra matrix no.pdf polynomial %N 11 %P 6206--6213 %R 10.1063/1.532624 %T The trace formulas yield the inverse metric formula %V 39 %X It is a well-known fact that the first and last nontrivial 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 the 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 four-dimensional resolvent formula allows an algebraic solution of the inverse metric problem in general relativity.

@article{silva98, abstract = {It is a well-known fact that the first and last nontrivial 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 the 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 four-dimensional resolvent formula allows an algebraic solution of the inverse metric problem in general relativity.}, added-at = {2016-04-10T12:01:56.000+0200}, author = {Silva, Ronaldo Rodrigues}, biburl = {https://www.bibsonomy.org/bibtex/2a315a7efa81bbc922f059e936e9d36a6/ytyoun}, doi = {10.1063/1.532624}, eid = {6206}, interhash = {3613f9ccb06d3f9956675d4507ef0ff2}, intrahash = {a315a7efa81bbc922f059e936e9d36a6}, journal = {Journal of Mathematical Physics}, keywords = {characteristic eigenvalues linear.algebra matrix no.pdf polynomial}, number = 11, pages = {6206--6213}, timestamp = {2016-04-10T12:01:56.000+0200}, title = {The trace formulas yield the inverse metric formula}, volume = 39, year = 1998 }