# nLab totally positive matrix

A matrix $A$ 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 total positivity is closely related to some phenomena in the theory of Lie groups and quantum groups.

• cluster algebra
• many lecture notes listed at a minicourse page on total positivity
• M. Skandera, Introductory notes on total positivity, ps, June 2003.
• Yuji Kodama, Lauren Williams, KP solitons and total positivity for the Grassmannian, arxiv/1106.0023

Created on June 2, 2011 at 12:37:52. See the history of this page for a list of all contributions to it.