Assess students' ability to analyze spectral decomposition, determine when a linear operator on a finite-dimensional vector space is diagonalizable, compute its Jordan canonical form, and relate algebraic vs. geometric multiplicities, minimal polynomial, generalized eigenspaces, Jordan chains, and nilpotent parts; include tasks requiring computation of eigenvalues/eigenvectors, construction of Jordan blocks, verification of similarity, and proofs of (non)diagonalizability over specified fields.