Sometimes, you can reorient your problem such that a matrix or tensor has only diagonal entries, making it easier to handle.

For example by choosing new unit vectors or by changing the set of functions describing the problem (whatever is the thing that the matrix or tensor is tied to).

sometimes when the stars align for a matrix A you can find an invertible matrix B such that B^-1⨯A⨯B gives a matrix that only has numbers on the diagonal and zeroes everywhere else.