Let Q be an orthogonal matrix Prove that Q2 1SolutionIf Q i

Let Q be an orthogonal matrix. Prove that ||Q||_2 = 1.

Solution

If Q is an orthogonal matrix then QQ^T = Q^T Q = I. Also, Q is necessarily symmewtric so that Q^T = Q . Then, Q² = QQ = QQ^T = I. Hence IIQ²II = II I II = 1.