The Pell and Pell-Lucas Numbers via Square Roots of Matrices

In this paper, the Pell and Pell-Lucas numbers with specialized rational subscripts are derived from general expressions by square roots of the matrices M-n and N-n. Besides, we reveal that the identities involving these numbers are produced by square roots matrices M-n/2 and N-n/2. Further we show that the matrices M-n and N-n are generalized to rational powers by using the Abel's functional equation.