Ranks of permutative matrices

Xiaonan Hu, College of William and Mary
Charles R. Johnson, College of William and Mary
Caroline E. Davis, College of William and Mary
Yimeng Zhang, College of William and Mary

Abstract

A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.