Gram-Schmidt

According to Wikipedia,

the GramSchmidt process is a method for orthonormalising a set of vectors in an inner product space,

Gram–Schmidt process, Wikipedia

Orthonormalising?

Not only is it “right,” it also makes your life a whole lot easier. If you don’t believe me, just watch the video on Coursera or have a go at it with our best friend, Salman Khan on Khan Academy.

We had to automate the process by writing a Python application. I”m not sure what I like best, learning about it, or coding about it. Me thinks I’ll take the latter.

Here’s a snippet:

def gsBasis(A) :
    B = np.array(A, dtype=np.float_)
    for i in range(B.shape[1]) :
        for j in range(i) :
            B[:, i] = B[:,i] - B[:,i] @ B[:,j] * B[:,j]
        if la.norm(B[:, i]) > verySmallNumber :
            B[:, i] = B[:, i] / la.norm(B[:, i])
        else :
            B[:, i] = np.zeros_like(B[:, i])
    return B

You can view the full code on Github.