Spectrally Arbitrary Zero Nonzero Patterns

Authors

Timothy Melvin, Washington State University & Carroll College

Document Type

Presentation Abstract

Presentation Date

5-6-2013

Abstract

A zero-nonzero pattern ℒ is a matrix whose entries are from the set {*,0}, where * denotes a nonzero entry. An n × n zero-nonzero pattern is called a spectrally arbitrary pattern (SAP) over the field F if for every monic polynomial p(t) with coefficients from F of degree n, there exists a matrix A over F with zero-nonzero pattern ℒ such that the characteristic polynomial of A is p(t).

The Nilpotent-Jacobian Method is a powerful tool developed to determine if a pattern is a SAP over ℝ (and ℂ). We will explore this method to determine what information can be gleaned when we look at a pattern over finite fields, ℚ, and extensions of ℚ.

Additional Details

Monday, 6 May 2013
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

Recommended Citation

Melvin, Timothy, "Spectrally Arbitrary Zero Nonzero Patterns" (2013). Colloquia of the Department of Mathematical Sciences. 429.
https://scholarworks.umt.edu/mathcolloquia/429