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Let T be an element of L(C^3) [complex 3-tuples] be the operator defined byT(z_1, z_2, z_3) = (z_2, z_3, z_1).
a) Write the matrix of T in the standard basis of C^3.
b Find all eigenvalues of T
c) Is there a basis of C^3 such that the matrix of T in that basis is diagonal? If your answer is "NO", explain why.
If your answer is "YES", write down the matrix in that basis.
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Use the permutation and combinations.
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Two linear systems.
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