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Consider the operator that is given by. M = 2 i -i 2 in the basis...

Consider the operator that is given by. M = 2 i

-i 2

in the basis {1} and {2} when they are assigned to {1,0} and {0,1} respectively.

a. What are the two new basis vectors for which M is diagonal?

b. Write the new pair of basis vectors both in ket notation as a linear combination of {1} and {2} and column notation with {1} and {2} assigned to {1,0} and {0,1} respectively. Label the two new basis vectors e1 and e2.

c. Explicitly show that the basis in which M is diagonal is orthogonal and explain why it had to be

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