Inner Product Spaces (Linear Algebra)?
Posted by James on March 6, 2014 · Leave a Comment
Question by HIYA: Inner Product Spaces (Linear Algebra)?
A vector space is valid on the interval (0, pi) with the inner product (f,g) in V. Consider the integral
S f(x)g(x) dx on the interval [0, pi]. Prove that cosx and sinx are orthogonal.
Best answer:
Answer by Lake R
You’re mangling the problem statement. What you are apparently asking about is a vector space of continuous functions on an interval with the usual inner product.
Recall that two vectors are orthogonal if their inner product is zero. So just integrate. (cos(x), sin(x)) =
?
? cos(x)sin(x) dx = ½sin²(?) – ½sin²(0) = 0.
0
That’s it.
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