In section 12.1 we showed you how to retain the canonical
directions as assignments and we went on to construct them as
quantities. We can do the same with the bearing vector: it is, after
all, a simple linear combination of elements in 
. To retain the
bearing we need to tell [B/D] before making the adjustment, and this is
achieved by issuing the command
BD>keep: b=Z 
This line informs [B/D] that the bearing for a subsequent adjustment is to be retained as an assignment named ``Z'' (here, too, we can choose another name if we wish). Suppose that we now effect the creation and retention of the bearing as an assignment by issuing another adjustment command:
BD>adjust: [B/D]
Firstly we can verify that [B/D] has added the newly created assignment that represents the bearing to the others that we created earlier, and saw in figure 20:
BD>look: (a)
Figure 23: Assigning the bearing
giving the output shown in figure 23. The first assignment
that we see corresponds to the bearing that we saw for the first time in
section 11.3, and we see also the assignments 
and
retained earlier. Now, just as we did for the canonical
directions, we will go on to build the bearing and then assess it as a
quantity by displaying its variance and covariances with 
and
:
BD>build: Z
BD>look: (v1) B, Z
Figure 24: Constructing the bearing
giving the output shown in figure 24. This shows that we
have indeed constructed 
, and have displayed the variance matrix
(with a variance for and covariances between and
deduced by [B/D] from the linear combination supplied) for ,
and . Notice how we modify the LOOK: command to
restrict the output to the detail that we want: we add a list of bases
and elements to the command
.
We can use this output to examine the covariances between the bearing
and the elements of , and verify that these covariances represent
the changes in expectation for each quantity due to the adjustment. We
can also verify another property, namely that the size of the adjustment
shown in figure 18 is equal to the prior variance of the
linear combination representing the bearing.