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In this paper, rectangular matrices whose minors of a given order have the same strict sign are considered and sufficient conditions for their recognition are presented. The results are extended to matrices whose minors of a given order have the same sign or are allowed to vanish. A matrix A is called oscillatory if all its minors are nonnegative and there exists a positive integer k such that A^k has all its minors positive. As a generalization, a new type of matrices, called oscillatory of a specific order, is introduced and some of their properties are investigated.
In this thesis, the recognition problem and the properties of eigenvalues and eigenvectors of matrices which are strictly sign-regular of a given order, i.e., matrices whose minors of a given order have the same strict sign, are considered. The results are extended to matrices which are sign-regular of a given order, i.e., matrices whose minors of a given order have the same sign or are allowed to vanish. As a generalization, a new type of matrices called oscillatory of a specific order, are introduced. Furthermore, the properties for this type are investigated. Also, same applications to dynamic systems are given.