In this chapter we begin an investigation into the possible relationships among the principal minors of TN matrices. A natural and important goal is to examine all the inequalities among the principal minors of TN matrices. More generally, we also study families of determinantal inequalities that hold for all TN matrices.
In 1893, Hadamard noted the fundamental determinantal inequality
holds whenever A=[aij] is a positive semidefinite Hermitian matrix. Hadamard observed ...