# Tag: Imperial College London

## Gram-Schmidt

According to Wikipedia,

the

Gram–Schmidt process, WikipediaGram–Schmidtprocess is a method for orthonormalising a set of vectors in an inner product space,

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.

## Special Matrices

In Coursera’s Mathematics for Machine Learning: Linear Algebra class, we learned all about matrices. One of my favorite is the row echelon form or REF.

I like it ‘cuz it sounds fancy and Trekkie-like.

Anyways, we had to write a Python application that converts a 4×4 matrix into row echelon form. There’s also a feature in there that catches errors in case of extra special matrices like singular matrices.

def fixRowTwo(A) : A[2] = A[2] - A[0] * A[2,0] A[2] = A[2] - A[1] * A[2,1] if A[2,2] == 0 : A[2] = A[2] + A[3] A[2] = A[2] - A[0] * A[2,0] A[2] = A[2] - A[1] * A[2,1] if A[2,2] == 0 : raise MatrixIsSingular() A[2] = A[2] / A[2,2] return A

You can view the full code on Github.