  The generalized complex numbers can be realized in terms of $2\times2$ or
higher-order matrices and can be exploited to get different ways of looking at
the trigonometric functions. Since Chebyshev polynomials are linked to the
power of matrices and to trigonometric functions, we take the quite natural
step to discuss them in the context of the theory of generalized complex
numbers. We also briefly discuss the two-variable Chebyshev polynomials and
their link with the third-order Hermite polynomials.
