On k -circulant matrices involving the Jacobsthal numbers

• Autores: Biljana Radicic
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 60, Nº. 2, 2019, págs. 431-442
• Idioma: inglés
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• Resumen

  • Let k be a nonzero complex number. We consider a k-circulant matrix whose first row is (J1, J2, . . . , Jn), where Jn is the n th Jacobsthal number, and obtain the formulae for the eigenvalues of such matrix improving the formula which can be obtained from the result of Y. Yazlik and N. Taskara [J. Inequal. Appl. 2013, 2013:394, Theorem 7]. The obtained formulae for the eigenvalues of a k-circulant matrix involving the Jacobsthal numbers show that the result of Z. Jiang, J. Li, and N. Shen [WSEAS Trans. Math. 12 (2013), no. 3, 341–351, Theorem 10] is not always applicable. The Euclidean norm of such matrix is determined. We also consider a k-circulant matrix whose first row is (J −1 1 , J−1 2 , . . . , J−1 n ) and obtain the upper and lower bounds for its spectral norm