Circulant type matrices have become an important tool in solving fractional order differential equations. In this paper, we consider the circulant and left circulant and -circulant matrices with the Jacobsthal and Jacobsthal-Lucas numbers. First, we discuss the invertibility of the circulant matrix and present the determinant and the inverse matrix. Furthermore, the invertibility of the left circulant and -circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the left circulant and -circulant matrices by utilizing the relation between left circulant, -circulant matrices, and circulant matrix, respectively.
"On Jacobsthal and Jacobsthal-Lucas Circulant Type Matrices." Abstr. Appl. Anal. 2015 (SI12) 1 - 11, 2015. https://doi.org/10.1155/2015/418293