An algorithmic approach to simultaneous triangularization (Q1020928)

The problem of determining whether or not a set of matrices, denoted by \(S\), admits a simultaneous triangularization is a long studied problem. This paper presents an algorithm to solve this problem. In order to apply this algorithm, one must have an algorithm for computing a common eigenvector for a set of matrices. To this end, one can run the \textit{D. Shemesh} algorithm [Linear Algebra Appl. 62, 11--18 (1984; Zbl 0556.15006)] for all pairs of matrices in \(S\) and bisect the results.