Abstract:
The class of square real matrices of order n having a positive determinant and all other
minors up to order n − 1 nonpositive are called sign regular matrices with signature
(−1, . . . , −1, 1). In this thesis, such matrices are introduced and a characterization of
them is presented which provides an easy test for their recognition based on the so-called
the Cauchon Algorithm. The value of the entry (2, 2) of the matrix resulting upon
application of the Cauchon algorithm to such a sign regular matrix plays a fundamental
role in our characterization. Therefore, the possible values of the entry (2, 2) are
explored. Finally, it is shown that all matrices lying between two matrices of this class
with respect to the so-called checkerboard ordering are contained in this class, too.
