We first prove that equation 3.2:

is the solution to the system of the following equations:

We assume here that the weight vector is a column vector with the same dimensionality as .

At first we combine equations A.2, A.4 and A.5. They yield

We can further manipulate the norm appearing on the right hand side of the equation.

Here we have used the fact that .
The term does not depend on *z*, and therefore it can
be left out without affecting the minimisation. We can now rewrite
the system of equations:

Without the constraint the solution would be . It is evident that equation A.1 gives the solution when we take the constraint into consideration.

Thu May 9 14:06:29 DST 1996