Eigenvalue Calculator

Enter a 2 x 2 or 3 x 3 matrix and this returns its eigenvalues, its real eigenvectors and the characteristic polynomial they come from. At these two sizes the polynomial is a quadratic and a cubic, so both are solved in closed form rather than by iteration, and a matrix whose roots are complex gets its conjugate pair reported rather than dropped. Real eigenvectors are scaled so their smallest nonzero entry is one, and an eigenvalue whose eigenspace has more than one dimension is named as such instead of being handed an arbitrary vector. Larger matrices are not offered, because past 3 x 3 there is no exact formula to fall back on.