Let 
, where 
has m components and
has n components.
Suppose we have k>n measurements 
, and wish to
recover 
.
Form matrices 
and 
by adjoining 
and 
, respectively. NOTE: 
is not square.
The 
matrix 
can be recovered as follows. Define an
error vector 
with m components:
Adjoining the k error vectors, we get
The sum of the squares of the errors is
Differentiate and equate to 0:
The term 
is the pseudoinverse
of 
.