Some properties of a special companion matrices and theirpowers

In this paper, we will discuss the properties of an interesting companion matrixthat is widely used in k-circulant matrices. Finding eigenvalues, singular values, qrfactorization, and many other interesting properties for this matrix and its integerpower are considered.

Keywords:

Companion matrix , k-ciculant matrix , qr factorization , Singular valuedecomposision.