What does multiplicity in eigenvalues mean?

[snoggerT]

Can someone please explain multiplicity to me? I've been able to solve the problems involving it, but I'm not quite sure what it means in terms of the eigenvalue. Thanks.

 

[Dick]

It means that the characteristic polynomial of the matrix of the linear transformation has a multiple root. I.e. x*(x-1)^2 has 1 as a double root (multiplicity 2). That's algebraic multiplicity. It may mean there are two linearly independent eigenvectors corresponding to the eigenvalue 1, but there might only be one. The latter concept is geometric multiplicity. In general algebraic multiplicity>=geometric multiplicity. Can't YOU look these things up? I think that's a faster way to get an answer.