• Support PF! Buy your school textbooks, materials and every day products Here!

Algebraic multiplicity

  • Thread starter dlevanchuk
  • Start date
  • #1
29
0

Homework Statement


I have a matrix A [1 -1 -1 -1; -1 1 -1 -1; -1 -1 1 -1; -1 -1 -1 1], its characteristic polynomial p(t) = (t + 2)(t-2)3, and given value of lambda = 2. I need to find basis for eigenspace, and determine algebraic and geometric multiplicities of labmda.


Homework Equations





The Attempt at a Solution



I did find the basis, and geometric multiplicity (the dimention of eigenspace).. but I cant figure out how to figure out algebraic multiplicity! I know the correct answer is 3, but why? i was trying to find simple explanation of alg. mult. on google, but the answer come up waay too tangled up for me to understand :-S

EDIT: Is it because the characteristic polynomial is p(t) = (t + 2)(t-2)3 and since my lambda = 2, i need to take (t-2)3 (which is t-2=0 => t=2), and the power is the value of algebraic mult...? am I on the right track?
 

Answers and Replies

  • #2
phyzguy
Science Advisor
4,372
1,352
You're on the right track. The multiplicity is basically how many "copies" of each eigenvalue exist. If each eigenvalue is unique, the multiplicity is 1. Since you have (t-2)^3, the eigenvalue of 2 is repeated three times, so the multiplicity is three, as you said.
 

Related Threads for: Algebraic multiplicity

  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
4K
Replies
4
Views
1K
Replies
1
Views
1K
Replies
2
Views
23K
Replies
3
Views
2K
Replies
6
Views
4K
  • Last Post
Replies
8
Views
1K
Top