Matrix Diagonalization Calculator

Enter a two by two or three by three matrix and this tool finds its eigenvalues from the characteristic polynomial, its eigenvectors as the nullspace of A minus xI, and then builds P from those eigenvectors and D from the eigenvalues. It multiplies P, D and the inverse of P back together and shows the product beside the original, because that product returning A is the only real check on the answer. When the eigenvectors do not span the space the matrix cannot be diagonalised, and the tool says which eigenvalue fell short and by how much instead of printing a P that does not work. A matrix whose characteristic polynomial has complex roots is reported the same way, since everything here stays in the real numbers.