Question: Gram Schmidt Orthogonalization With Function Spaces

I'm trying to orthonormalize the set of basis vectors of the form form p(x)*exp(-x^2/2), where p(x) is a polynomial of degree less than N.

The basis I'm using for this function space is |e1> = exp(-x^2/2), |e2> = x*exp(-x^2/2), |e3> = x^2 * exp(-x^2/2), and so on.


However the GramSchmidt procedure in the LinearAlgebra package only accepts vectors.

Can someone help me to get around this, and use some procedure to orthonormalize the first four bases for this function space?

One fix that I'm going to try is to use "four vectors" with the appropriate function bases in their corresponding positions and zeros elsewhere.

Would this be correct?


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