Chapter 12.2, Problem 6E

(a) Show that the determinant of a matrix in real Schur form is the product of the determinants of the $1\times 1$

and $2\times 2$

blocks on the main diagonal. (b) Show that the eigenvalues of a matrix in real Schur form are the eigenvalues of the $1\times 1$ and $2\times 2$ blocks on the main diagonal.