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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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