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Quick Stability Checks and Matrix Norms

Authors: Conlisk, John;

Quick Stability Checks and Matrix Norms

Abstract

Consider the difference equation system yt=b+Ayt-i; where yt is an nXl variable vector, b is an nXl constant vector and A is an nXn constant matrix. The fundamental necessary and sufficient stability condition for the system is /x(^)< 1, where [J.(A) is the modulus of the characteristic root of A of largest modulus. That is, IJ.(A) is the spectral radius of A, so-called because all roots of A lie on or within a circle of radius ix(A) in the complex plane. There exists a class of scalar real-valued functions of matrices called matrix norms; and any matrix norm/(y4) has the property iJ^(A)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
20
Average
Top 10%
Average
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