Composition Identities of Chebyshev Polynomials, via 2 × 2 Matrix Powers

Primo Brandi, Paolo Emilio Ricci
2020 Symmetry  
Starting from a representation formula for 2 × 2 non-singular complex matrices in terms of 2nd kind Chebyshev polynomials, a link is observed between the 1st kind Chebyshev polinomials and traces of matrix powers. Then, the standard composition of matrix powers is used in order to derive composition identities of 2nd and 1st kind Chebyshev polynomials. Before concluding the paper, the possibility to extend this procedure to the multivariate Chebyshev and Lucas polynomials is touched on.
doi:10.3390/sym12050746 fatcat:s3flr44hgvbmlcqbzxzba6zvmm