Normalizing a feature matrix

I was working on a side project and I started wondering about the normalization I was doing on a feature matrix.

Let's say I have an X by F feature matrix, where X is the numbers_of_samples, and F is the numbers_of_features. First, I am taking the principle components (however many is needed to reach 95% of the variance), then I am just running a GMM on it. It's just a proof of concept to show that there is something learnable.

Currently, I am normalizing each feature vector. Is this the right thing to be doing? Or should I be normalizing each sample?

Thanks in advance!