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‫Welcome back.

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‫Let's see now what the dimensions of Q double bar, T double bar and R double bar are.

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‫You know that this vector here is thirty six by one and since this vector here is transposed, then

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‫here you have one row and thirty six columns.

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‫It's this one here so you have one row and thirty six columns.

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‫That's this one here.

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‫X still the global transposed then X still the global is thirty six by one.

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‫That means that this matrix is thirty six by thirty six.

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‫And what about this sub matrix here.

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‫So see till transposed q C Tilde.

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‫Well you know the C till there.

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‫It's three rows and nine columns as we have discussed before.

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‫That means the C till the transposed is nine rows and three columns and Q is three by three.

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‫So the dimensions match.

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‫So if you cancel out these threes here and these threes here, then you're left with nine by nine.

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‫So each sub matrix here is nine by nine.

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‫And that means that these zeroes here, they're are also zero matrices.

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‫They're nine by nine zero matrices.

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‫And what about T double bar then?

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‫You know that you're cuttable bar is thirty six by thirty six.

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‫Well let's look at this element here.

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‫Q Times see till the Q is three by three and then see till there is three by nine.

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‫So you cancel all the threes and you're left with three by nine.

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‫So this sub matrix here is three by nine and that also means that you're zero matrix.

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‫Here's three by nine.

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‫That means that the T double bar is twelve by thirty six.

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‫And then what about the R double bar.

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‫Will you know that R is a three by three wait matrix.

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‫And so that means that your zero matrix is also three by three.

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‫So you are double bar is twelve by twelve and you can see that each term in this cost function will

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‫result in a scalar in the end.

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‫So let's take this first term here, here.

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‫This augment the state vector which is global and transposed.

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‫It's one times thirty six like this.

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‫Then your matrix, the global weight matrix.

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‫Q double barrel is thirty six by thirty six and then there's global LGMA, the state vector is thirty

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‫six by one.

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‫And so you cancel out these thirty sixes here and then you're left with one by one which is a scalar.

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‫Similarly the second term is like this.

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‫So you have this transposed reference value vector which is one row and twelve columns.

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‫Then this one here is thirty six rows and one column.

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‫So in the end you have one times twelve which is this one here, one row twelve columns.

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‫Then this t double bar matrix is twelve by thirty six like this and then this vector here is thirty

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‫six by one.

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‫So you cancel out the twelfth, you cancel out the thirty sixes and you're left with one by one which

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‫is a scalar and then it's the same thing with the last term.

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‫Here you have a twelve by one vector, here you have a one by twelve vector and then here this R double

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‫bar is twelve by twelve and so you have one row twelve columns, then twelve by twelve and then twelve

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‫by one.

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‫And so you cancel out these twelfths and you are left with one by one.

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‫So that's a scalar here.

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‫So now you have an idea of the Diemen.

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‫A chance for these vectors and matrices, and so in the end, you can rewrite this entire cost function

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‫in a compact form like this, Jay Prime equals that would be your first term.

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‫That would be your second term.

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‫And don't forget about the minus sign here and that would be your third term here.

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‫So this is a compact way to rewrite J.

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‫Prime.