Let T be' a linear e)perate>r on an n-dimensional real inner product space V. Suppe)se

Chapter 6, Problem 17

(choose chapter or problem)

Let T be' a linear e)perate>r on an n-dimensional real inner product space V. Suppe)se that T is not the identity. Prove the following results. (a) If a, is odd, then T can be e'xpressexl as the1 e-emiposite of at most one reflection anel at most \(n 1) rotations. (b) If /? is even, then T can be1 e'xpresse>el as the' colllpe)site, of at most | n rotations e>r as the ce)iupe)sitc of one inflection and at most ^(n 2) rotations