‫Welcome back.
‫If you remember from the previous course, then in this mathematical manipulation process, you ended
‫up with some terms that were constant.
‫They did not have any independent variables in them.
‫And so we said that we could simply make them zero because from the optimization point of view, they
‫did not matter.
‫If the goal is to maximize or minimize something, then constant terms play no role.
‫Kind of like if you have these two functions, this one right here y equals x squared plus three.
‫And this one here Y equals x squared.
‫In both cases, the X value for the minimum point is zero.
‫The constant term three here in the first function does not play a role.
‫If you want to find your X men, so you might as well just eliminate it and similarly in the cost function.
‫These are the terms that we will eliminate because they are constant terms.
‫They play no role in finding the independent variables in the cost function for the minimum j value.
‫We can get rid of these terms here that I have crossed out with white and then also these ones here
‫that I have crossed out with green, but only when your eye equals zero, because only then this variable
‫here becomes your present state because it's going to be K plus zero.
‫So it's going to be X augmented vector.
‫Supcase is going to be your present value and therefore you know what it is.
‫It's not a variable, it's a constant.
‫If your eye is greater than zero, then this X still there will become a variable because it's going
‫to become a future state and you don't know the future state, and therefore it's an independent variable.
‫And then you cannot cross out these terms here in green.
‫And now the new cost function that is without the constant terms, we will name that J.
‫Prime.
‫It's not Jay anymore, because Jay was a cost function with those constant terms.
‫But if you get rid of those constant terms, then actually you have a different cost function.
‫It is a matter for optimization, but still it's a different cost function and therefore we give it
‫a different name.
‫Jay Prime.
‫So to be fair, I should have put a prime here as well.
‫Y prime equals x squared because it's a different function.
‫Next, we want to get rid of this summation sign here.
‫That's what we want to get rid of in the previous course.
‫I showed you how to get rid of the summation sign by converting these equations here with several terms
‫into a vector matrix form like here.
‫So you see this spectrum matrix form is equivalent to this form here with many terms, and that is equivalent
‫to this compact form with the summation sine from Y equals one up until three.