Explicit form of determinants and inverse matrices of Tribonacci r-circulant type matrices

On determinants, inverses, norms, and spread of skew circulant matrices involving the product of Pell and Pell-Lucas numbers

“…On the other hand, the importance of determinants, inverses, norms and spread in special matrix analysis, several authors [4,6,10,11,13,17,20,23,[28][29][30][31][32] have done some research on these special matrices. Recently, Jiang and Hong [12] studied the explicit form of determinants and inverses of Tribonacci r-circulant type matrices, while Zheng and Shon [36] gave the exact determinants and inverses of generalized Lucas skew circulant type matrices. Besides, Shen et al [24] did some work on the explicit determinants and inverses of circulant matrices with Fibonacci and Lucas numbers.…”

A New Method of Matrix Decomposition to Get the Determinants and Inverses of r -Circulant Matrices with Fibonacci and Lucas Numbers

“…Carmona et al [17] propose the necessary and sufficient conditions for the invertibility of some circulant matrices that depend on three parameters and compute explicitly the inverse of a general symmetric, circulant, and tridiagonal matrix. Hong and Jing [18] investigate the invertibility of the Tribonacci r-circulant matrix and show the determinant and the inverse matrix based on constructing the transformation matrices. He et al [19] and Türkmen and Gökbas [20] study the spectral norm of r-circulant matrices with Fibonacci and Lucas numbers and Pell and Pell-Lucas numbers, respectively.…”

Determinants, inverses, norms, and spreads of skew circulant matrices involving the product of Fibonacci and Lucas numbers

“…Recently, some authors have done some research on circulant matrices involving some famous numbers about their determinants, inverses, some norms, and spreads [2,5,10,11,13,18,20,24,25]. Recently, Zheng and Shon [30] studied the exact determinants and inverses of generalized Lucas skew circulant type matrices, while Jiang and Hong [12] gave that of Tribonacci r-circulant type matrices. What's more, AhmetÍpek [9] investigated an improved estimation for spectral norms of circulant matrices with classical Fibonacci and Lucas number entries.…”