Eigenvalues + Algebraic/Geometric Multiplicity


by verd
Tags: eigenvalues, multiplicity
verd
verd is offline
#1
May1-07, 05:45 PM
P: 146
I'm studying for a linear algebra final, and I'm looking over an old final our prof gave us and I've come across something I don't remember ever hearing anything about... Here's the problem:

Write down a matrix A for the following condition:
A is a 3x3 matrix with lambda=4 with algebraic multiplicity 3 and with geometric multiplicity 1.

...I don't have a problem with eigenvalues or anything, but I don't believe he ever mentioned algebraic multiplicity or geometric multiplicity. Is this another concept in linear algebra?? Or is this something way simple that I'm looking way too far into.

...What does he mean by algebraic multiplicity and geometric multiplicity??


Thanks!
Phys.Org News Partner Science news on Phys.org
Cougars' diverse diet helped them survive the Pleistocene mass extinction
Cyber risks can cause disruption on scale of 2008 crisis, study says
Mantis shrimp stronger than airplanes
Dick
Dick is offline
#2
May1-07, 06:17 PM
Sci Advisor
HW Helper
Thanks
P: 25,173
Algebraic multiplicity is easy. It's the multiplicity of the root in the characteristic polynomial. I checked wikipedia (always a good first stab) for geometric multiplicity and it says that it is the dimension of the eigenspace. In other words, there is only one linearly independent eigenvector with value 4.
boof
boof is offline
#3
May6-11, 04:58 AM
P: 1
http://www.youtube.com/watch?v=13r9QY6cmjc


Register to reply

Related Discussions
multiplicity of a gas Introductory Physics Homework 1
multiplicity of a pole General Math 8
multiplicity in eigenvalues Calculus & Beyond Homework 1
Geometric Topology Vs. Algebraic Topology. General Math 1
numerical solutions of system of nonlinear algebraic equations nonlinear algebraic eq General Math 6