Typically,
, *i.e.*, the number of frequency constraints is much
greater than the number of design variables (filter taps). In these
cases, we have an *overdetermined* system of equations (more
equations than unknowns). Therefore, we cannot generally satisfy all
the equations, and we are left with minimizing some error criterion to
find the ``optimal compromise'' solution.

In the case of least-squares approximation, we are minimizing the
*Euclidean distance*, which suggests the following geometrical
interpretation:

This diagram suggests that the error vector
is *orthogonal* to
the column space of the matrix
, hence it must be orthogonal to each
column in
.

This is how the *orthogonality principle* can be used to
derive the fact that the best least squares solution is given by

Note that the pseudo-inverse
*projects* the vector
onto the column space of
.

**In Matlab:**

`x = A b``x = pinv(A) * b`

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