Hi,

Really unsure about how to do this question, so any help/answers/links to a similar thread would be appreciated.

landa is an eigenvalue of a linear map T:V to V (V over C). Suppose the eigenspace W has dimension r. Prove that the characteristic polynomial CA(x) of a nxn matrix A representing T is divisiblr by ((landa)-x)^r, and deduce that r is less than or equal to the multiplicity of landa as an eigenvalue of A.

Thankyou