I am brushing up this topic. I want to verify both orthogonality between two functions and an orthogonal set ALWAYS have to be with respect to the specified interval.......[a,b].(adsbygoogle = window.adsbygoogle || []).push({});

That is, a set of {1, ##\cos n\theta##, ##\sin m\theta##} is an orthogonal set IF AND ONLY IF ##\theta## on [##-\pi,\;\pi##]. Where n and m are 0, 1, 2, 3, 4.........

{##\cos n\theta##, ##\sin m\theta##} is not an Orthogonal set on [##0,\;\pi##]}

Also, the interval [a,b] does not have to be symmetrical to define orthogonality or an orthogonal set......That is...... a doesn't has to equal to b.

Thanks

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# Orthogonality and orthogonal set.

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