| |
|
|
| |
Volume 9, Issue 4, Article 92 |
|
|
|
|
|
| |
Multiplicative Principal-Minor Inequalities for A Class of Oscillatory Matrices
|
| |
|
Authors: |
Xiao Ping Liu, Shaun M. Fallat, |
|
| |
|
Keywords:
|
Totally positive matrices; Determinant; Principal minor; Bidiagonal factorization, Determinantal inequalities; Generators. |
|
| |
|
Date Received:
|
29/11/06 |
|
| |
|
Date Accepted:
|
22/06/08 |
|
| |
|
Subject Codes: |
15A15, 15A48.
|
|
| |
|
Editors: |
Alexander M. Rubinov (1940-2006), Chi-Kwong Li, |
|
| |
|
|
|
|
|
| |
|
Abstract: |
A square matrix is said to be totally nonnegative (respectively, positive) if all of its minors are nonnegative (respectively, positive). Determinantal inequalities have been a popular and important subject, especially for positivity classes of matrices such as: positive semidefinite matrices, M matrices, and totally nonnegative matrices. Our main interest lies in characterizing all of the inequalities that exist among products of both principal and non-principal minors of certain subclasses of invertible totally nonnegative matrices. This description is accomplished by providing a complete list of associated multiplicative generators.
|
|
|
|
|
|
| |
|
|
|
|
| |
|
|
|
|
|
Home
