  Several new spectral properties of the normalized Laplacian defined for
oriented hypergraphs are shown. The eigenvalue $1$ and the case of duplicate
vertices are discussed; two Courant nodal domain theorems are established; new
quantities that bound the eigenvalues are introduced. In particular, the
Cheeger constant is generalized and it is shown that the classical Cheeger
bounds can be generalized for some classes of hypergraphs; it is shown that a
geometric quantity used to study zonotopes bounds the largest eigenvalue from
below, and that the notion of coloring number can be generalized and used for
proving a Hoffman-like bound. Finally, the spectrum of the unnormalized
Laplacian for Cartesian products of hypergraphs is discussed.
