In mathematics, the GelfandâZeitlin system (also written GelfandâZetlin system, GelfandâCetlin system, GelfandâTsetlin system) is an
integrable system on conjugacy classes of Hermitian matrices. It was introduced by Guillemin and Sternberg (
1983), who named it after the
GelfandâZeitlin basis, an early example of
canonical basis, introduced by
I. M. Gelfand and
M. L. Cetlin in 1950s. Kostant and Wallach (
2006) introduced a complex version of this integrable system.