On k-circulant matrices with the Lucas numbers
Copyright policy )On k-circulant matrices with the Lucas numbers
Let k be a nonzero complex number. In this paper, we determine the eigenvalues of a k-circulant matrix whose first row is (L1,L2,..., Ln), where Ln is the nth Lucas number, and improve the result which can be obtained from the result of Theorem 7. [28]. The Euclidean norm of such matrix is obtained. Bounds for the spectral norm of a k-circulant matrix whose first row is (L-11, L-12,..., L-1n ) are also investigated. The obtained results are illustrated by examples.
Eigenvalues, singular values, and eigenvectors, Toeplitz, Cauchy, and related matrices, Euclidean norm, spectral norm, eigenvalues, Fibonacci and Lucas numbers and polynomials and generalizations, Norms of matrices, numerical range, applications of functional analysis to matrix theory, \(k\)-circulant matrix, Lucas numbers
Eigenvalues, singular values, and eigenvectors, Toeplitz, Cauchy, and related matrices, Euclidean norm, spectral norm, eigenvalues, Fibonacci and Lucas numbers and polynomials and generalizations, Norms of matrices, numerical range, applications of functional analysis to matrix theory, \(k\)-circulant matrix, Lucas numbers
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