A fast computation for the determinant, inverse, and eigenvalues of skew circulant matrices involving Fibonacci numbers.

In this article, the determinant, inverse, and eigenvalues of skew circulant matrices with entries in the first row having the formation of Fibonacci sequence are formulated explicitly in a simple form in one theorem. The method for deriving the formulation of the determinant and inverse is simply using traditional elementary row or column operations which is directed to to get a simpler equivalent matrix. For the eigenvalues, the known formulation from the case of general skew circulant matrices is simplified by considering the speciality of the sequence and using cyclic group properties of unit circles in the complex plane. Then, the algorithms of those formulations are constructed and they perform as a fast computation. [ABSTRACT FROM AUTHOR]