4.II.11E
(i) Let be an -dimensional inner-product space over and let be a Hermitian linear map. Prove that has an orthonormal basis consisting of eigenvectors of .
(ii) Let be another Hermitian map. Prove that is Hermitian if and only if .
(iii) A Hermitian map is positive-definite if for every non-zero vector . If is a positive-definite Hermitian map, prove that there is a unique positivedefinite Hermitian map such that .
Typos? Please submit corrections to this page on GitHub.