Please answer the given question in detail.

Let U = {A E M3(R) | A is orthogonally diagonalizable} and let W = {A E M3(R) | A is lower triangular} You may take for granted that U and W are subspaces of M3 (R). Prove that U ~ W by constructing an explicit isomorphism from U to W or from W to U. Pick whatever direction you find the easiest. :)