‫Welcome back.
‫Let's see now what the dimensions of Q double bar, T double bar and R double bar are.
‫You know that this vector here is thirty six by one and since this vector here is transposed, then
‫here you have one row and thirty six columns.
‫It's this one here so you have one row and thirty six columns.
‫That's this one here.
‫X still the global transposed then X still the global is thirty six by one.
‫That means that this matrix is thirty six by thirty six.
‫And what about this sub matrix here.
‫So see till transposed q C Tilde.
‫Well you know the C till there.
‫It's three rows and nine columns as we have discussed before.
‫That means the C till the transposed is nine rows and three columns and Q is three by three.
‫So the dimensions match.
‫So if you cancel out these threes here and these threes here, then you're left with nine by nine.
‫So each sub matrix here is nine by nine.
‫And that means that these zeroes here, they're are also zero matrices.
‫They're nine by nine zero matrices.
‫And what about T double bar then?
‫You know that you're cuttable bar is thirty six by thirty six.
‫Well let's look at this element here.
‫Q Times see till the Q is three by three and then see till there is three by nine.
‫So you cancel all the threes and you're left with three by nine.
‫So this sub matrix here is three by nine and that also means that you're zero matrix.
‫Here's three by nine.
‫That means that the T double bar is twelve by thirty six.
‫And then what about the R double bar.
‫Will you know that R is a three by three wait matrix.
‫And so that means that your zero matrix is also three by three.
‫So you are double bar is twelve by twelve and you can see that each term in this cost function will
‫result in a scalar in the end.
‫So let's take this first term here, here.
‫This augment the state vector which is global and transposed.
‫It's one times thirty six like this.
‫Then your matrix, the global weight matrix.
‫Q double barrel is thirty six by thirty six and then there's global LGMA, the state vector is thirty
‫six by one.
‫And so you cancel out these thirty sixes here and then you're left with one by one which is a scalar.
‫Similarly the second term is like this.
‫So you have this transposed reference value vector which is one row and twelve columns.
‫Then this one here is thirty six rows and one column.
‫So in the end you have one times twelve which is this one here, one row twelve columns.
‫Then this t double bar matrix is twelve by thirty six like this and then this vector here is thirty
‫six by one.
‫So you cancel out the twelfth, you cancel out the thirty sixes and you're left with one by one which
‫is a scalar and then it's the same thing with the last term.
‫Here you have a twelve by one vector, here you have a one by twelve vector and then here this R double
‫bar is twelve by twelve and so you have one row twelve columns, then twelve by twelve and then twelve
‫by one.
‫And so you cancel out these twelfths and you are left with one by one.
‫So that's a scalar here.
‫So now you have an idea of the Diemen.
‫A chance for these vectors and matrices, and so in the end, you can rewrite this entire cost function
‫in a compact form like this, Jay Prime equals that would be your first term.
‫That would be your second term.
‫And don't forget about the minus sign here and that would be your third term here.
‫So this is a compact way to rewrite J.
‫Prime.