Non-Hermitian matrices

A non-Hermitian matrix is a type of mathematical object used to describe systems where energy or information isn't conserved symmetrically. Unlike Hermitian matrices, which have properties ensuring symmetrical behavior and real eigenvalues, non-Hermitian matrices don't follow these rules, often leading to complex eigenvalues. This makes them useful for modeling dissipative systems, open quantum systems, or processes with gain and loss, such as certain optical or mechanical systems. They help scientists understand a broader range of real-world phenomena where symmetry and conservation don't strictly apply.