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In this paper a state space formula is derived for the least squares solution X of the corona type Bezout equation G(z)X(z) = I  m . Here G is a (possibly non-square) stable rational matrix function. The formula for X is given in terms of the matrices appearing in a state space representation of G and involves the stabilizing solution of an associate discrete algebraic Riccati equation. Using these matrices, a necessary and sufficient condition is given for right invertibility of the operator of multiplication by G. The formula for X is easy to use in Matlab computations and shows that X is a rational matrix function of which the McMillan degree is less than or equal to the McMillan degree of G.

Right Invertible Multiplication Operators and Stable Rational Matrix Solutions to an Associate Bezout Equation, I: The Least Squares Solution