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

Question: Let A be a 2 2 matrix with Schur decomposition UTUH and suppose that t12 0. Show that (a) The eigenvalues of A

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.

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