Title: Part IB
Tags: Endomorphisms

Q: Theorem. Let V be a vector space over \(\mathbb{C}\). \(\alpha \in \text{End}(V)\) with \(m_{\alpha}(t) = (t-\lambda_1)^{c_1} \dots (t-\lambda_k)^{c_k}\) where \(\lambda_1 , \dots , \lambda_k\) are distinct. Then \[V = \bigoplus_{i=1}^n V_i\] where \(V_i = \text{Ker}((\lambda_i I - A)^{c_i})\). These \(V_i\) are called generalised eigenspaces.
A: No proof.