in reply to Help with Matrix math!

If you set aside for a moment the constraint on the vector `x`, then the problem of maximizing
`x _{i}D_{ij}x_{j}`
(a sum over repeated indices is implied) translates, upon taking the derivative with respect to

`x`, into the equation

_{i}`D`. This is a special form of the eigenvalue equation for the matrix

_{ij}x_{j}= 0`D`, with the eigenvalue being 0. In order for non-trivial solutions, the matrix

`D`cannot have an inverse, so it's determinant must vanish. Finding the eigenvectors can be done with PDL; see Mastering Algorithms with Perl for a discussion. The Math::Cephes::Matrix module can also do this for real symmetric matrices. Generally, the components of the eigenvectors found in this way are not completely determined; by convention, the normalization

`x`is imposed.

_{i}x_{i}= 1
*Update:* The preceding needs to be augmented by a
test on the
Hessian of the matrix to determine what type of
critical point is present.