Hello,

I was just wondering what non-degenerate means??

I would like to show that if h is an element of (r,s) = (0,2) Tensor
and h is non-degenerate (?) then det(h _a_b) =/= 0. h_a_b are the
components.

Well I was thinking if something is non-degenerate, does it mean the
matrix of components is non-singular?? If so, then that would mean
det(h _a_b) =/=0 since if the matrix is non-singular = the matrix has
an inverse = det =/= 0.

Can someone clearify this??

Thanks

Jack Smith:
Hello,

I was just wondering what non-degenerate means??


Each eigenvalue is associated with only one eigenvector.


I would like to show that if h is an element of (r,s) = (0,2) Tensor
and h is non-degenerate (?) then det(h _a_b) =/= 0. h_a_b are the
components.

Well I was thinking if something is non-degenerate, does it mean the
matrix of components is non-singular?? If so, then that would mean
det(h _a_b) =/=0 since if the matrix is non-singular = the matrix has
an inverse = det =/= 0.

It means the determinant of the matrix M, |M - \lambda I| = 0.