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Pauli Z Matrix


The Pauli z matrix, denoted Z, sigma_z, or sigma_3, is the third of the three Pauli matrices,

 Z=[1 0; 0 -1].

It is both a Hermitian matrix and a unitary matrix, with eigenvalues +1 and -1. Its square is the identity matrix.

It is implemented in the Wolfram Language as PauliMatrix[3].


See also

Pauli Matrices, Pauli X Matrix, Pauli Y Matrix

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References

Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 211-212, 1985.IBM Quantum. "Pauli Operations and Observables." https://quantum.cloud.ibm.com/learning/en/courses/foundations-of-quantum-error-correction/stabilizer-formalism/pauli-operations-and-observables.

Cite this as:

Weisstein, Eric W. "Pauli Z Matrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PauliZMatrix.html

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