Look up something on Tikhonov regularization, also known as ridge regression in machine learning. This is a standard technique (but I agree that the explanation in that notebook is somewhat poor).

Technically speaking, it does not affect the numerical stability of that algorithm, but it modifies the problem to a more well-conditioned one, from $\min \|\Phi \theta - y\|^2$ to $$\min \|\Phi \theta - y\|^2 + \kappa \|y\|^2.$$

Look up something on Tikhonov regularization, also known as ridge regression in machine learning. This is a standard technique (but I agree that the explanation in that notebook is somewhat poor).

Technically speaking, it does not affect the numerical stability of that algorithm, but it modifies the problem to a more well-conditioned one, from $\min \|\Phi \theta - y\|^2$ to $$\min \|\Phi \theta - y\|^2 + \kappa \|\theta\|^2.$$