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Unformatted text preview: B k = 0 for some k ≤ n . Suppose A ∈ C n × n (not necessarily Hermitian) and show that A = A D + A N where A D is a nondefective, i.e., diagonalizable, matrix, A N is a nilpotent matrix and A D A N = A N A D . 1 Problem 1.6 Let A ∈ C n × n and deﬁne H A = 1 2 ( A + A H ) and S A = 1 2 ( A-A H ) called the Hermitian part and skew Hermitian parts of A respectively. Clearly, A = H A + S A . Show that A is a normal matrix if and only if the matrix product of H A and S A commutes, i.e., H A S A = S A H A . Problem 1.7 Problem 7.1.1 Golub and Van Loan p. 318 Problem 1.8 Problem 7.1.5 Golub and Van Loan p. 318 Problem 1.9 Problem 7.1.8 Golub and Van Loan p. 318 2...
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- Fall '06
- Matrices, Diagonalizable matrix, Orthogonal matrix, Normal matrix