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For a sequence of polynomials $\{p_k(t)\}$ in one real or complex variable,where $p_k$ has degree $k$, for $k\ge 0$, we find explicit expressions andrecurrence relations for infinite matrices whose entries are the coefficients$d(n,m,k)$, called linearization coefficients, that satisfy $$ p_n(t)p_m(t)=\sum_{k=0}^{n+m} d(n,m,k) p_k(t).$$  For any pair of polynomial sequences $\{u_k(t)\}$ and $\{p_k(t)\}$ we findinfinite matrices whose entries are the coefficients $e(n,m,k)$ that satisfy$$p_n(t) p_m(t)=\sum_{k=0}^{n+m} e(n,m,k) u_k(t).$$  Such results are obtained using a matrix approach. We also obtain recurrencerelations for the linearization coefficients, apply the general results togeneral orthogonal polynomial sequences and to particular families oforthogonal polynomials such as the Chebyshev, Hermite, and Charlier families.

Linearization and connection coefficients of polynomial sequences: A matrix approach