What are perpendicular functions and how are they used in function spaces?

[Silverious]

Does anyone know anything about perpendicular functions? I just kinda stumbled onto it thinking about perpendicular tanget lines. Could anyone shed light on the situation?

 

[Tide]

I'm not sure what you mean by "perpendicular functions" but you might be thinking about "orthogonal functions." The (overly) simple definition of orthogonal functions is that the integral of their product over a domain is zero.

 

[Silverious]

Maybe I should consider it more and post a more detailed question. I'll do that.

 

[phoenixthoth]

If the two functions belong to an inner product space, they are perpendicular if their dot product is zero just like how any two vectors are perpendicular if their dot product is zero.

An orthonormal basis is a set of vectors that are all perpendicular and have unit length. In R^3 Euclidean space, (1,0,0), (0,1,0), and (0,0,1) are in such a basis. In a function space, a space with functions in it, you might have a list of orthonomoral functions (which are still vectors). Then you can project another function onto the space using the orthonormal basis. For example, if you project e^x onto the space generated by {1,x,x^2} which BTW is not itself an o.n. basis, then you get a 2nd degree polynomial that approximates e^x. Perpedicular functions run amok in this process. . .