Write this matrix explicitly if both bases are orthonormal.

Question

Let \(\left\{w_{1}, w_{2}, \ldots, w_{n}\right\}\) be yet another basis for \(\mathbb{R}^{n}\). Find a matrix that maps the \(\left\{v_{j}\right\}\) basis to the \(\left\{w_{j}\right\}\) basis. Write this matrix explicitly if both bases are orthonormal.