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‫Welcome back.

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‫If you remember from the previous course, then in this mathematical manipulation process, you ended

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‫up with some terms that were constant.

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‫They did not have any independent variables in them.

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‫And so we said that we could simply make them zero because from the optimization point of view, they

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‫did not matter.

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‫If the goal is to maximize or minimize something, then constant terms play no role.

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‫Kind of like if you have these two functions, this one right here y equals x squared plus three.

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‫And this one here Y equals x squared.

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‫In both cases, the X value for the minimum point is zero.

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‫The constant term three here in the first function does not play a role.

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‫If you want to find your X men, so you might as well just eliminate it and similarly in the cost function.

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‫These are the terms that we will eliminate because they are constant terms.

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‫They play no role in finding the independent variables in the cost function for the minimum j value.

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‫We can get rid of these terms here that I have crossed out with white and then also these ones here

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‫that I have crossed out with green, but only when your eye equals zero, because only then this variable

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‫here becomes your present state because it's going to be K plus zero.

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‫So it's going to be X augmented vector.

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‫Supcase is going to be your present value and therefore you know what it is.

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‫It's not a variable, it's a constant.

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‫If your eye is greater than zero, then this X still there will become a variable because it's going

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‫to become a future state and you don't know the future state, and therefore it's an independent variable.

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‫And then you cannot cross out these terms here in green.

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‫And now the new cost function that is without the constant terms, we will name that J.

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‫Prime.

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‫It's not Jay anymore, because Jay was a cost function with those constant terms.

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‫But if you get rid of those constant terms, then actually you have a different cost function.

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‫It is a matter for optimization, but still it's a different cost function and therefore we give it

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‫a different name.

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‫Jay Prime.

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‫So to be fair, I should have put a prime here as well.

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‫Y prime equals x squared because it's a different function.

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‫Next, we want to get rid of this summation sign here.

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‫That's what we want to get rid of in the previous course.

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‫I showed you how to get rid of the summation sign by converting these equations here with several terms

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‫into a vector matrix form like here.

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‫So you see this spectrum matrix form is equivalent to this form here with many terms, and that is equivalent

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‫to this compact form with the summation sine from Y equals one up until three.