Singular Values of k-Fibonacci and k-Lucas Hankel Matrices
نویسندگان
چکیده
An exact formula was recently obtained for the spectral norms of the Lucas and Fibonacci Hankel matrices [1], and also for the Lucas and Fibonacci Toeplitz matrices [4]. These results put finishing touches on the works initiated in [2] and [3]. On another front, bounds were found for the spectral norms of k-Fibonacci and k-Lucas Toeplitz matrices [7]. In this paper, we present the exact value for the spectral norms of these Toeplitz matrices. We also obtain the non-trivial eigenvalues of any even dimensional Hankel matrix built with a sequence that satisfies si + ksi+1 = si+2, making it possible to calculate the spectral norm of any even dimensional Hankel or Toeplitz matrix built with such a sequence.
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