We're interested in looking at various forms of

the regularized problem, I described in the previous slide.

We'll, we'll introduce functional j of x which depend

on values norms and we'll start with the L2 norm.

So, the L2 norm of a vector is defined here, it's also called the Euclidean norm.

I'm sure that you've encountered this many times, in the past.

So for example, if we are given a vector with elements 3,

4, 0, a three by one vector, then its L2 norm is simply

equal to the square root of 3 squared plus 4 squared plus 0

squared, so the square root of 25, which is equal to 5.

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Let's look at how the unit bowl, looks, with respect to the L2 norm.

So, let's look in two dimensions, it is easier to visualize.

So, let's look at, the gaze where the, L2 norm squared of the vector is equal to 1.

And in two dimensions, this means that x1 squared plus x two squared, equals to 1.

So this is clearly the equation, of a circle in two

D, or a hydrosphere if we are in the undimensional space.

So with, our axis here, x1 and x2.

This is the, unit circle, according to the

L2 norm, so the radius here is equal to 1.

We are interested in solving this Constraint Optimization problem.

We want to minimize the L2 norm of the vector, subject

to the constraint of the vector, the solution satisfies, the data.