Jordan's Canonical Form Just Doesn't Compute
By Cleve Moler, MathWorks
Matrices and differential equations are the fundamental mathematical tools in MATLAB® and Simulink®. The Jordan Canonical Form (JCF) is the key relationship between matrices and differential equations and yet MATLAB doesn’t use the JCF in any of its computations.
In this article, originally published in 1994, Cleve Moler explains how any kind of error—uncertainty in experimental data, arithmetic roundoff error, linearization of nonlinear functions—completely changes the JCF and the transformations that generate it. Cleve notes that this extreme sensitivity to perturbation is the main difficulty with the JCF, pointing out that the numerically reliable approach is to avoid the JCF altogether.
Published 1994 - 92030v00