Algebraic Muliplicity of an EigenVector

[Ghost101]

1.Hello! I am having trouble understanding what A.M. is in the problem which asks, "Find the eigenvalues and eigenvectors associated with the matrix and find the a.m and g.m of each;

for example...

-1 0 0
1 0 1 - I * Lambda
0 2 1

The Attempt at a Solution

gives

(-1 - lambda)(-2 + Lambda)(1 + Lambda) = 0

Lambda = -1, -1, -2

The Eigenvector for -1 is t*

0
-1
1 Now it says the a.m. is two? but I don't understand why? :S

the g.m is obviously one because there is only one column.

 

[vela]

Tell us the definition of algebraic multiplicity.

 

[Ghost101]

wiki;

They are called multiplicities: the algebraic multiplicity of an eigenvalue is defined as the multiplicity of the corresponding root of the characteristic polynomial.

So... its basically how many unique roots there are? is that why its 2?

or does it mean that the eigenvalue is repeated twice so its 2?

 

[vela]

To do math, you have to know definitions. If you don't know what a term means, instead of guessing, look it up. It's not enough to find just one definition, like the one in Wikipedia, if you don't understand what it's saying. Keep looking until you find a definition or example that makes it clear.

http://tutorial.math.lamar.edu/Classes/DE/LA_Eigen.aspx

I know I could just tell you the answer, but I want to encourage you to develop habits so you can find answer to these really basic questions yourself, especially these days where looking things up online is so easy to do. Also, you presumably spent a good chunk of money on a textbook, so use it. I know students often don't like to read a text because they find it confusing, but working through this confusion is often where the real learning occurs. And, again, it's a skill you need to develop to succeed in your studies.

 

[Ghost101]

Ah yes! I see now, a good link.

and yes I'm sorry for the trivial question, my textbook doesn't cover it unfortunately ;(

Thanks again!