inverse, several times, the following is a simple mathematical technique 
that allows the modification of the matrix inverse of the normal equations 
due to deleting some of the observation equations. 
4.2 Modified Inverse of the Coefficient Matrix of Normal Equations After 
deleting Some of the Original Observation Equations 
Equation 4.08 can be rewritten as: 
4.13 
N D 
-P 
• • • • 
where 
4.14 
N 
B* U F 
4.15 
P 
• • • • 
The solution of equation 4.13 is: 
4.16 
D 
• • • • 
in which N -1 is assumed to have been previously evaluated and on the 
basis of a total of n object points. We now divide n into two sets: 
q points which are to be deleted and p points which are retained. (Note 
that p must yield a number of equations that are equal to or more than 
the number of unknowns.) The corresponding sets of observation equations 
are: 
for q points V+BC-CD = -F 
4.17 
• • • • 
for p points V+BD-CÏÏ = -F 
4.18 
In view of the summation scheme given in the previous section and 
expressed by equations 4.12 and 4.10, the system of normal equations 
corresponding to 4.17 and 4.18 may be written as: