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(d)
Show that the matrix
6.
is unitary for every real value of . .
In Exercises 7–12 find a unitary matrix that diagonalizes , and determine
7.
8.
9.
10.
11.
12.
Show that the eigenvalues of the symmetric matrix
13.
are not real. Does this violate Theorem 10.6.6?
14.
(a) Find a matrix that is both Hermitian and unitary and whose entries are not all real numbers.
