A sign pattern is a sign pattern if has no zero entries. allows orthogonality if there exists a real orthogonal matrix whose sign pattern equals . Some sufficient conditions are given for a sign pattern matrix to allow orthogonality, and a complete characterization is given for sign patterns with to allow orthogonality.
Let be the set of nonnegative integers and the ring of integers. Let be the ring of matrices over generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of yields that the subrings generated by them coincide. This subring is the sum of the ideal consisting of...
A complete list of positive Tits-sincere one-peak posets is provided by applying combinatorial algorithms and computer calculations using Maple and Python. The problem whether any square integer matrix is ℤ-congruent to its transpose is also discussed. An affirmative answer is given for the incidence matrices and the Tits matrices of positive one-peak posets I.
It is known that a real symmetric circulant matrix with diagonal entries , off-diagonal entries and orthogonal rows exists only of order (and trivially of order ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries and any complex entries of absolute value off the diagonal. As a particular case, we consider matrices whose...