PERTURBATIONS, SINGULAR-VALUES, AND RANKS OF PARTIAL TRIANGULAR MATRICES

Questions regarding minimal representations of perturbations of discre te systems lead to the study of perturbations of lower triangular part ial matrices and their minimal rank completions. Distance to the set o f lower triangular partial matrices having minimal ranks smaller than a given integer is given in terms of (suitably generalized) singular n umbers. Minimal ranks of lower triangular partial matrices in an arbit rary small neighborhood of a given lower triangular partial matrix are identified. The results are applied to minimal representations of dis crete systems.