- #1
KD-jay
- 7
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Homework Statement
1) Let's say I was trying to find the eigenvalues of a matrix and came up with the following characteristic polynomial:
λ(λ-5)(λ+2)
This would yield λ=0,5,-2 as eigenvalues. I'm kinda thrown off as to what the algebraic multiplicity of the eigenvalue 0 would be? I'm pretty sure it would just be 1 but I think I've misheard my instructor say otherwise during one example.
2) Let's say I have the following characteristic polynomial of matrix A.
(λ-2)(λ-4)(λ-α), where α is any number.
If I were trying to figure out values of α that make A diagonalizable, it would be any values of alpha that makes that particular eigenvalue different from 2 or 4. What if λ-α=0 did make λ equal 2 or 4? Do I have to check the geometric multiplicities for λ=2,4, or can I automatically assume that the matrix would not be diagonalizable.
Homework Equations
det(A-λI) = 0 where A is a matrix and λ are the eigenvalues A