What is the easiest way to find a square inverse metric?

Answer 1

if A is a non-singular square matrix then the inverse of A,denoted by a^-1 is equal to

A^-1=(1/!A!) adj A
method to find the inverse of Square Matrix A.
(1) Evaluate the value of !A! (only if !A! is non zero we can find A^-1)
(2) Find the co factors of elements of matrix A and write down the matrix formed by cofactors of elements A as
A11 A12 A13
A21 A22 A23
A31 A32 A33

(3)write down the adj A as
transpose of
A11 A12 A13
A21 A22 A23
A31 A32 A33

as

A11 A21 A31
A12 A22 A23
A13 A23 A33

(4) By formulawrite down A^-1=(1/!A!)(adj A)

Answer 2

If you're asking what I think you're asking, ther's a pretty good article on self-commuting metric tensors at
http://en.wikipedia.org/wiki/Metric_tensor


Doug