Computing the Kalman decomposition: An optimal method

In this paper we describe a method for computing the complete Kalman decomposition of a linear dynamical system, and we show that this method is optimal in a certain sense. Specifically, we describe an algorithm to compute a mapping that, when applied to the original system, yields a complete Kalman decomposition. We show that, of all transformations that yield a Kalman decomposition, the one we construct here has the lowest condition number.