A generalisation of Gram-Schmidt’s orthonogonalisation process
I just read up about the Gram-Schmidt orthogonalization process.
Say we have as an orthonormal basis for a subspace. Now let for ANY , where is the vector space. The set is orthonormal.
$a$ needn’t be a vector from , where is spanned by .
We require to be from only because we want to make the orthonormal set span a larger vector space.