Unformatted text preview: Math 602 (2011) Homework 3 1. Let A be a self-adjoint matrix. Show that there is a self-adjoint matrix B
B 3 = A(A − 2I )(A − 3I )
What are the eigenvalues of B in terms of the eigenvalues of A? Will B
commute with A?
2. Assume that A is a symmetric matrix with eigenvalues not equal to 3.
True or false? The matrices A(A − 2I ) and (A − I )(A − 3I )−1 commute.
3. Show that if N is a normal matrix then N x = N ∗ x for all vectors x.
And from Strang, 3rd Ed. (refer to the handout) p.319,
solve: 5.3, 5.4, 5.5, 5.19, 5.20(a)(b). 1 ...
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