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This work provides two results obtained as a consequence of an inversionformula for Toeplitz matrices with real symbol. First we obtain an asymptoticexpression for the minimal eigenvalues of a Toeplitz matrix with a symbolwhichis periodic, even and derivable on $[0, 2\pi[$. Next we prove that a Toeplitzband matrix with a symbol without zeros on the united circle is invertible withan inverse which is essentially a band matrix. As a consequence of this laststatement we give an asymptotic estimation for the entries of the inverse of aToeplitz matrix with a regular symbol.

Expression asymptotique des valeurs propres d'une matrice de Toeplitz \`a symbole r\'eel