TY - JOUR

T1 - On the Lengths of Pairs of Complex Matrices of Size at most Five

AU - Longstaff, William

AU - Niemeyer, Alice

AU - Panaia, Oreste

PY - 2006

Y1 - 2006

N2 - The length of every pair {A, B} of n×n complex matrices is at most 2n − 2, if n ≤ 5. That is, for n ≤ 5, the (possibly empty) words in A, B of length at most 2n − 2 span the unital algebra generated by A, B. For every positive integer m there exist m×m complex matrices C, D such that the length of the pair {C, D} is 2m – 2.

AB - The length of every pair {A, B} of n×n complex matrices is at most 2n − 2, if n ≤ 5. That is, for n ≤ 5, the (possibly empty) words in A, B of length at most 2n − 2 span the unital algebra generated by A, B. For every positive integer m there exist m×m complex matrices C, D such that the length of the pair {C, D} is 2m – 2.

U2 - 10.1017/S0004972700035462

DO - 10.1017/S0004972700035462

M3 - Article

VL - 73

SP - 461

EP - 472

JO - Bulletin of Australian Mathematical Society

JF - Bulletin of Australian Mathematical Society

SN - 0004-9727

ER -