The Gaussian Fibonacci Skew-Circulant Type Matrices
نویسندگان
چکیده
Abstract: Let be a Gaussian Fibonacci skew-circulant matrix, and be a Gaussian Fibonacci left skew-circulant matrix, and both of the first rows are , where is the th Gaussian Fibonacci number, and is a nonnegative integer. In this paper, by constructing the transformation matrices, the explicit determinants of and are expressed. Moreover, we discuss the singularities of these matrices and the inverse matrices of them are obtained.
منابع مشابه
Exact Determinants of the RFPrLrR Circulant Involving Jacobsthal, Jacobsthal-Lucas, Perrin and Padovan Numbers
Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...
متن کاملOn the Determinants and Inverses of Skew Circulant and Skew Left Circulant Matrices with Fibonacci and Lucas Numbers
Abstract: In this paper, we consider the skew circulant and skew left circulant matrices with the Fibonacci and Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrix and present the determinant and the inverse matrix by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices are also discussed. We obtain the determ...
متن کاملOn the Norms and Spreads of Fermat, Mersenne and Gaussian Fibonacci RFMLR Circulant Matrices
Abstract: In this paper, we consider norms and spreads of RFMLR circulant matrices involving the Fermat, Mersenne sequences and Gaussian Fibonacci number, respectively. Firstly, we reviewed some properties of the Fermat, Mersenne sequences, Gaussian Fibonacci number and RFMLR circulant matrices. Furthermore, we give lower and upper bounds for the spectral norms and spread of these special matri...
متن کاملA NOTE ON CERTAIN MATRICES WITH h(x)-FIBONACCI POLYNOMIALS
In this paper, it is considered a g-circulant, right circulant, left circulant and a special kind of tridiagonal matrices whose entries are h(x)-Fibonacci polynomials. The determinant of these matrices is established and with the tridiagonal matrices we show that the determinant is equal to the nth term of the h(x)-Fibonacci polynomials.
متن کاملSpectral norms of circulant-type matrices involving some well-known numbers
In this paper, we investigate spectral norms for circulant-type matrices, including circulant, skewcirculant and g-circulant matrices. The entries are product of binomial coefficients with Fibonacci numbers and Lucas numbers, respectively. We obtain identity estimations for these spectral norms. Employing these approaches, we list some numerical tests to verify our results.
متن کامل