A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

The past decades have witnessed an explosion of interest in topological materials, and a lot
of mathematical concepts have been introduced in condensed matter physics. Among them …

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-
reaching physical consequences observable in a range of dissipative settings are reviewed …

A unique feature of non-Hermitian systems is the skin effect, which is the extreme sensitivity
to the boundary conditions. Here, we reveal that the skin effect originates from intrinsic non …

Non-Hermiticity enriches topological phases beyond the existing Hermitian framework.
Whereas their unusual features with no Hermitian counterparts were extensively explored, a …

In the past few years, concepts from non-Hermitian (NH) physics, originally developed within
the context of quantum field theories, have been successfully deployed over a wide range of …

Non-Hermiticity gives rise to unique topological phases that have no counterparts in
Hermitian systems. Such intrinsic non-Hermitian topological phases appear even in one …

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical
dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering …

Non-Hermitian Hamiltonians are generally sensitive to boundary conditions, and their
spectra and wave functions under open boundary conditions are not necessarily predicted …

Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized
to be not always detrimental but can be exploited to achieve non-Hermitian topological …