ItemThen \(V=(v_1 | v_2 | v_3 | \dots | v_n)\) is the matrix whose columns are the preimages of the principal semiaxes, i.e., \(A v_i = \sigma_i u_i.\) It should be clear that the \(\{v_i\}\) form an orthonormal set, so \(V^{-1}=V^\star.\)