I am trying to prove that a matrix that is both "unitary and upper triangular" must be a diagonal matrix.
I am thinking that the fact that columns of all unitary matrices form an orthonormal basis of F^n will ensure that all columns of this matrix are mutually orthogonal.
Also, the fact that the matrix is upper triangular will then give me the required result....but I am trying to derive a formal proof. Please suggest if my approach is OK.
Thanks in advance.