If "A" is a real matrix, its Jordan form can still be non-real. Instead of representing it with complex eigenvalues and 1's on the superdiagonal, as discussed above, there exists a real invertible matrix "P" such that "P"−1"AP" = "J" is a real block diagonal matrix with each block being a real Jordan block. A real Jordan block is either identical to a complex Jordan block (if the corresponding eigenvalue formula_21 is real), or is a block matrix itself, consisting of 2×2 blocks (for non-real eigenvalue formula_43 with given algebraic multiplicity) of the form