Abstract
AbstractA 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.
Highlights
By a permutative matrix we mean an m-by-n matrix whose entries are chosen from among n independent variables over the nonnegative real numbers in such a way that each row is a di erent permutation of the n variables
Associated with each permutative matrix A is a collection P(A) of permutative matrices resulting from consistent substitution of distinct positive real numbers for the variables
We identify the two major ways that we have found for a permutative matrix to be identically singular
Summary
Johnson Coll William & Mary, Dept Math, POB 8795, Williamsburg, VA 23187 USA. Davis Coll William & Mary, Dept Math, POB 8795, Williamsburg, VA 23187 USA. Yimeng Zhang Coll William & Mary, Dept Math, POB 8795, Williamsburg, VA 23187 USA.
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