Assess students' ability to compute the matrix exponential exp(A) and the principal matrix square root A^{1/2} for finite-dimensional Hermitian matrices using spectral (eigen) decomposition. Tasks should include: diagonalizing a given Hermitian matrix A = U diag(λ_i) U*, explicitly computing exp(A)=U diag(e^{λ_i}) U* and A^{1/2}=U diag(√λ_i) U* when applicable; explaining existence and uniqueness of the principal square root (requirement of nonnegative eigenvalues), how to treat negative eigenvalues or complex square roots, and verifying key properties (commutation with A, relation exp(A) positive definite, norms). Include one explicit 3×3 computation and one short justification of the functional calculus step and a brief note on numerical stability/conditioning of the spectral approach.