Refined Inertia of Matrix Patterns

نویسندگان

  • Kevin N. Vander Meulen
  • Jonathan Earl
  • Adam Van Tuyl
  • ADAM VAN TUYL
چکیده

This paper explores how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. It demonstrates that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike what happens for nonzero patterns. A class of patterns is developed that are refined inertially arbitrary but not spectrally arbitrary, making use of the property of a properly signed nest. The paper includes a characterization of the inertially arbitrary and refined inertially arbitrary patterns of order three, as well as the patterns of order four with the least number of nonzero entries.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Refined inertially and spectrally arbitrary zero-nonzero patterns

The refined inertia of a matrix is a quadruple specifying its inertia and additionally the number of its eigenvalues equal to zero. Spectral properties, especially the refined inertias, of real matrices with a given zero-nonzero pattern are investigated. It is shown that every zero-nonzero refined inertially arbitrary pattern of order 4 or less is also spectrally arbitrary. Irreducible and redu...

متن کامل

Generating potentially nilpotent full sign patterns

A sign pattern is a matrix with entries in {+,−, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentially...

متن کامل

Refined inertias of tree sign-patterns

The refined inertia (n+, n−, nz, 2np) of a real matrix is the ordered 4-tuple that subdivides the number n0 of eigenvalues with zero real part in the inertia (n+, n−, n0) into those that are exactly zero (nz) and those that are nonzero (2np). For n ≥ 2, the set of refined inertias Hn = {(0, n, 0, 0), (0, n − 2, 0, 2), (2, n − 2, 0, 0)} is important for the onset of Hopf bifurcation in dynamical...

متن کامل

Ela Refined Inertias of Tree Sign Patterns

The refined inertia (n+, n−, nz, 2np) of a real matrix is the ordered 4-tuple that subdivides the number n0 of eigenvalues with zero real part in the inertia (n+, n−, n0) into those that are exactly zero (nz) and those that are nonzero (2np). For n ≥ 2, the set of refined inertias Hn = {(0, n, 0, 0), (0, n − 2, 0, 2), (2, n − 2, 0, 0)} is important for the onset of Hopf bifurcation in dynamical...

متن کامل

Ela Generating Potentially

A sign pattern is a matrix with entries in {+, −, 0}. A full sign pattern has no zero entries. The refined inertia of a matrix pattern is defined and techniques are developed for constructing potentially nilpotent full sign patterns. Such patterns are spectrally arbitrary. These techniques can also be used to construct potentially nilpotent sign patterns that are not full, as well as potentiall...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2017