------6.2 Orthogonal basis
Orthogonal basis is a thing
Orthonormal basis is a thing
Given an orthogonal basis, it is very easy to write a vector is terms of that basis. Even better if it is orthonormal. This agrees with standard basis.
Given any finite dimension vector, you can constr
Do example with (1,1)/sqrt(2), (1,-1)/sqrt(2) and (3,4)
Talk about Fourier coefficients.
These are just the coefficients against an orthonormal basis.
exp(int) is orthonormal.
Orthogonal complement is a thing. It is a subspace.
The kernel is the orthogonal complement of the row space.
Given any subspace of W of V. V is the direct sum of W and its orthogonal complement.