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