Orthogonal Matrices


Selected Homework 9.
(1) Determine which of the following matrices are orthogonal matrices.

matrix([[0, 1, 1/2*2^(1/2)], [1, 0, 0], [0, 0, 1/2*2^(1/2)]]), matrix([[-1/2*2^(1/2), 1/6*6^(1/2), 1/3*3^(1/2)], [0, -1/3*6^(1/2), 1/3*3^(1/2)], [1/2*2^(1/2), 1/6*6^(1/2), 1/3*3^(1/2)]]), matrix([[1/2,...

(2) Show that following matrices are orthogonal in three different ways.

matrix([[4/5, 0, -3/5], [-9/25, 4/5, -12/25], [12/25, 3/5, 16/25]]), matrix([[1/3, 2/3, 2/3], [2/3, -2/3, 1/3], [-2/3, -1/3, 2/3]])