Properties of numerical algorithms related to computing controllability

The numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations. In particular, the numerical rank of a matrix, the numerical stability of algorithms, the sensitivity of problems, and the scaling of problems are discussed. A numerically stable algorithm is given for computing controllability, but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful, and this appears to be an open computational problem.