Abstract
Skew circulant and circulant matrices have been an ideal research area and hot issue for solving various differential equations. In this paper, the skew circulant type matrices with the sum of Fibonacci and Lucas numbers are discussed. The invertibility of the skew circulant type matrices is considered. The determinant and the inverse matrices are presented. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, the maximum row sum matrix norm, and bounds for the spread of these matrices are given, respectively.
Highlights
As is well-known, skew circulant and circulant matrices play a crucial role for solving various differential equations
We define a sum of Fibonacci and Lucas skew circulant matrix which is an n × n complex matrix with following form: SCirc (L1, L2, . . . , Ln)
A sum of Fibonacci and Lucas skew left circulant matrix is given by SLCirc (L1, L2, . . . , Ln)
Summary
As is well-known, skew circulant and circulant matrices play a crucial role for solving various differential equations. We define a sum of Fibonacci and Lucas skew circulant matrix which is an n × n complex matrix with following form: SCirc A sum of Fibonacci and Lucas skew left circulant matrix is given by SLCirc Let {Ln} be the sum of Fibonacci and lucas numbers; n (i) ∑Li = Ln+2 − 4, (6)
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