Inner product spaces
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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!
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Solution Summary
This is a proof of orthogonality and unit vectors, and shows how to determine distance between vectors.
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