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 .