Stata The Stata listserver
[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

st: RE: "Diagonalizing" a non-symmetric matrix

From   "Nick Cox" <[email protected]>
To   <[email protected]>
Subject   st: RE: "Diagonalizing" a non-symmetric matrix
Date   Thu, 2 Oct 2003 16:06:37 +0100

I understood Mitra to want a matrix with
the eigenvalues along the diagonal. That's
what was asked for. It's true, as I understand
it, that diagonalization as such is a different

Of course, if the eigenvalues have imaginary
parts it is rather difficult to do anything
with that matrix in Stata, but I didn't think it
necessary to spell that out. Either way, -geneigen-
would seem to be the first step in Stata, even
if one can't go beyond it.

[email protected]

> -----Original Message-----
> Clyde Schechter
> Yesterday, Mitra Pinaki asked for help in diagonalizing a
> non-symmetric
> matrix.  Nick Cox pointed him to Kit Baum's -geneigen-
> which will, indeed,
> calculate the eigenvalues of a non-symmetric matrix.  But that won't
> diagonalize the matrix.  In fact, it's fairly simple linear
> algebra to show
> that any matrix of real numbers which _can_ be diagonalized
> is necessarily
> symmetric!  So it's unclear what M.P. is trying to do.
> The most that can be done with a non-symmetric matrix is to
> identify its
> eigenvalues and eigenvectors (which, due to non-symmetry, will have
> cardinality strictly less than the rank of the matrix) and
> then create a
> diagonal matrix out of those.  But that diagonal matrix
> will be of smaller
> rank than the original, and is not a conjugate of the
> original matrix.  Any
> conjugate of the original which does diagonalize as much as
> possible will
> still have a piece which has non-zero elements off the diagonal.

*   For searches and help try:

© Copyright 1996–2024 StataCorp LLC   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index