Let A be a 2 2 matrix with Schur decomposition UTUH and suppose that t12 0 Show that (a) The eigenvalues of A are 1 t11 and 2 t22 (b) u1 is an eigenvector of A belonging to 1 t11 (c) u2 is not an eigenvector of A belonging to 2 t22 ...

a A and T are similar and hence have the same eigenvalues Since T is triangular its eigenv ...

Let A be a 2 2 matrix with Schur decomposition UTUH and suppose that t12

Question:

Let A be a 2 × 2 matrix with Schur decomposition UTUH and suppose that t12 ≠ 0. Show that
(a) The eigenvalues of A are λ1 = t11 and λ2 = t22.
(b) u1 is an eigenvector of A belonging to λ1 = t11.
(c) u2 is not an eigenvector of A belonging to λ2 = t22.