My main question to the forum surrounds the definition of orthonormality with real valued functions (refer to Image 1&2).I understand the implications of the dot product in vector space and the vector being orthonormal if it is of unit length, but I don't see how this relates to functions devoid of vectors or how it can be said that for example the Fourier series can represent any function with a orthonormal set of Trig function using the definition in Image 1&2.(adsbygoogle = window.adsbygoogle || []).push({});

I understand the orthonormality definition of a function with respect to another represents orthogonality in some way and that and an Infinite series of discretely independent functions should be able to represent any function, but I find it hard to dissect the definition below and how this all relates to vector space.

Thanks in advanced

p.s this is my first post so sorry if its in the wrong section or not explicit enough tell me and I will change it =).

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# The Orthonormality of real valued Functions

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