# Ellipsoid algebra: converting forms

1. Aug 8, 2011

### d_forage

I have a matrix D (it happens to be in R^(nxm) where n>>m, but I don't think that is relevant at this point). I also have a vector t in R^n.

I am interested in rewriting the set

{x | (Dx-t)'(Dx-t) <= c} in standard ellipsoid form: --> {x | (x-z)'E(x-z)<=b} where E is an mxm positive semi definite matrix. So, I'd like to write z, E and b in terms of D, t, and c.

Is there an algebraic way to do this?

(The application area is radiation therapy, D represents the so-called dose-influence matrix.)

2. Aug 8, 2011

### I like Serena

Last edited by a moderator: Apr 26, 2017