Question: paractice not for mark 5. Let V = C4 with the standard inner product. Let he the stande ordered basis for V. Let T be

paractice not for mark

5. Let V = C4 with the standard inner product. Let he the stande ordered basis for V. Let T be the linear operator on V such that 000% 00250 [=o2ts 17000 (a) Show that T is a normal operator. (b) Find a unitary matrix P and a diagonal matrix D such that PAP' = D. (c) Compute the spectral decomposition of T, that is nd the formula for each orthog- onal projection that occurs in the spectral decomposition of T, and express T as a linear combination of these orthogonal projections

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