I would like to have full detailed solutions( prefer those thatwrite on a separate sheet of paper to show all steps)
For this problem, the norm A of a matrix A is the norm induced by the standard inner product, (A, B) = tr(BTA). Let P be an n x n orthogonal matrix and let A be an n x m matrix. Prove that PA = A . Let Q be an m x m orthogonal matrix and let A be an n x m matrix. Prove that AQ = A . Let A and B be orthogonally similar matrices, that is, assume that there exists an orthogonal matrix P with PTAP = B. Show that A = B . Let A = and Let B = Show that while there exists an invertible matrix C with B = C-l AC, there does not exist an orthogonal matrix P with B = PTAP.
