# Eigenvalue Problem for 2×2 Hermitian Matrices

Eigenvalue Problem for 2×2 Hermitian Matrices

An Hermitian matrix (=) has real eigenvalues and mutually orthogonal eigenvectors, which can be chosen to be normalized. This Demonstration considers the case of Hermitian matrices, which has important applications in the study of two-level quantum systems. For a selected Hermitian matrix, the graphic shows the equations satisfied by the two eigenvalues, with their corresponding orthonormalized eigenvectors.

n×n

M

ji

*

M

ji

n

n

2×2

2×2