References
- A. Ben-Israel and T.N.E. Greville, Generalized Inverses. Theory and Applications, Springer-Verlag, New York, 2003.
- P. Catarino, H. Campos, and P. Vasco, On the Mersenne sequence, Ann. Math. Inform. 46 (2016), 37–53.
- T. Goy, On new identities for Mersenne numbers, Appl. Math. E-Notes 18 (2018), 100–105.
- F.A. Graybill, Matrices with Applications in Statistics, Wadsworth Advanced Books and Software, Belmont, CA, 1983.
- C.-H. Guo and N.J. Higham, A Schur-Newton method for the matrix pth root and its inverse, SIAM J. Matrix Anal. Appl. 28 (2006), no. 3, 788–804.
- N.J. Higham and L. Lin, A Schur-Padé algorithm for fractional powers of a matrix, SIAM J. Matrix Anal. Appl. 32 (2011), no. 3, 1056–1078.
- N.J. Higham and L. Lin, On pth roots of stochastic matrices, Linear Algebra Appl. 435 (2011), no. 3, 448–463.
- D. Kalman and R. Mena, The Fibonacci numbers-exposed, Math. Mag. 76 (2003), no. 3, 167–181.
- T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley-Interscience, New York, 2001.
- H. Özdemir, S. Karakaya, and T. Petik, Notes on generalized Fibonacci numbers and matrices, Honam Math. J. 44 (2022), no. 4, 473–484.
- P.J. Psarrakos, On the mth roots of a complex matrix, Electron. J. Linear Algebra 9 (2002), 32–41.
- C.R. Rao and S.K. Mitra, Generalized inverse of a matrix and its applications, in: L.M. Le Cam et al. (eds.), Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability. Vol. I: Theory of Statistics, University of California Press, Berkeley, CA, 1972, pp. 601–620.
- P. Ribenboim, My Numbers, My Friends: Popular Lectures on Number Theory, Springer-Verlag, New York, 2000.
- Z. Şiar and R. Keskin, Some new identities concerning generalized Fibonacci and Lucas numbers, Hacet. J. Math. Stat. 42 (2013), no. 3, 211–222.
- M.I. Smith, A Schur algorithm for computing matrix pth roots, SIAM J. Matrix Anal. Appl. 24 (2003), no. 4, 971–989.
- S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section. Theory and Applications, Ellis Horwood Ltd., Chichester, 1989.
- F.V. Waugh and M.E. Abel, On fractional powers of a matrix, J. Amer. Statist. Assoc. 62 (1967), no. 319, 1018–1021.