An eigenvalue is the scalar that multiplies an eigenvector when a unitary transformation is applied, leaving the vector otherwise unchanged. For a unitary, its absolute value is 1, so λ = e^(2πiθ), where θ is the corresponding real-valued eigenphase. section 5.3
Examples from quantum gates
For the Z gate, |0⟩ has eigenvalue 1 and eigenphase 0, while |1⟩ has eigenvalue −1 and eigenphase 0.5. The INC unitary also has eigenvalues i and −i, with eigenphases 0.25 and 0.75; the T gate has eigenvalue e^(iπ/4) and eigenphase 0.125 for |1⟩. section 5.3
