In C[-pi, pi] with inner product defined by (6), show that cos mx and sin nx are orthogonal and that both are unit vectors. Determine the distance between the two vectors.
(6) (f,g) = (1/pi)* the integral from -pi to +pi of f(x)g(x)dx
This is all from Linear Algebra With Applications by Steven J. Leon, Sixth Edition. Thanks!© BrainMass Inc. brainmass.com March 4, 2021, 5:37 pm ad1c9bdddf
This is a proof of orthogonality and unit vectors, and shows how to determine distance between vectors.