Abstract
The length of a pair of matrices is the smallest integer l l such that words in the matrices with at most l l factors span the unital algebra generated by the pair. Upper bounds for lengths have been much studied. If B B is a rank one n × n n\times n (complex) matrix, the length of the irreducible pair { A , B } \{A,B\} is 2 n − 2 2n-2 and the subwords of A n − 1 B A n − 2 A^{n-1}BA^{n-2} form a basis for M n ( C ) M_n(\mathbb {C}) . New examples are given of irreducible pairs of n × n n\times n matrices of length n n . There exists an irreducible pair of 5 × 5 5\times 5 matrices of length 4 4 . We begin the study of determining lower bounds for lengths.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
