Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897817 | Linear Algebra and its Applications | 2018 | 22 Pages |
Abstract
Let AâRnÃn be a totally nonnegative matrix with principal rank p, that is, every minor of A is nonnegative and p is the size of the largest invertible principal submatrix of A. We introduce the sequence of the first p-indices of A as the first initial row and column indices of a pÃp invertible principal submatrix of A with rank p. Then, we study the linear dependence relations between the rows and columns indexed by the sequence of the first p-indices of A and the remaining of its rows and columns. These relations, together with the irreducibility property of some submatrices of A, allow us to present an algorithm that calculates the maximum rank of A as a function of the distribution of the first p-indices. Finally, we present a method to construct nÃn totally nonnegative matrices with given rank r, principal rank p and a specific sequence of the first p-indices.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Rafael Cantó, Ana M. Urbano,