Answered: Consider the matrix 0 -i 0' M = |i 0,… | bartleby

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1. Please answer the question completely and accurately with full detailed steps since I need to understand the concept. (The more explanation the better.)

Consider the matrix

\[
\mathbf{M} = \begin{pmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}
\]

(a) Find the eigenvalues and corresponding properly normalized eigenvectors of \(\mathbf{M}\).

(b) Find the unitary matrix \(\mathbf{U}\) that diagonalizes \(\mathbf{M}\).

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