A matrix over the field of real numbers is totally positive (resp. totally nonnegative) if every minor (= determinant of any submatrix) is a positive (resp. nonnegative) real number. Total positivity implies a number of remarkable properties; for example all eigenvalues are distinct and positive. George Lusztig discovered that this classical total positivity is a related to more general total positivity phenomena in the theory of Lie groups and quantum groups.
Last revised on September 17, 2023 at 13:57:13. See the history of this page for a list of all contributions to it.