matrix manipulation

[lisa]

hello,
please, how can I define in Eviews a matrix where all the eigenvectors are <1.
Thanks.

[EViews Chris]

I'm afraid you'll have to provide more details as to what you're trying to acheive.

A diagonal matrix with values less than one along the diagonal is an example of a matrix with eigenvalues less than one, but I doubt that this is what you have in mind.

Are you trying to take an existing matrix and 'scale it down' so that the eigenvalues of the new matrix are less than one? Are you trying to generate a 'random' matrix with eigenvalues less than one?

Both of these operations will probably revolve around expressions (assuming you're interested in a symmetric matrix) of the form:

S = V D V'

where D is diagonal and V is orthonormal.

The pre-and-post multiplication of D by the orthonormal matrix V preserves the eigenvectors of D (which are simply the diagonal elements), so you can generally get to where you want to go by playing about with this expression.

[lisa]

I want to generate a random matrix with eigenvalues less than one.
thanks.