A novel adaptive algorithm for an array using directional elements called a hybrid smart antenna system is proposed. The algorithm controls the element patterns on the basis of an objective function composed of eigenvalues of a covariance matrix. A high and stable array output signal-to-interference-plus-noise ratio (SINR) is achieved by improving both the received powers and the spatial correlation coefficient between incident waves, without prior knowledge such as directions-of-arrival (DOA), channel state information (CSI), or training signals. The characteristics of the proposed algorithm are theoretically and numerically clarified for a simple case involving two incident waves. Convergence with least mean squares (LMS) algorithm is found to be as fast as that with recursive least squares (RLS) algorithm in this system. Also, simulation for statistical performance evaluation is carried out in comparison with a conventional system. Furthermore, a method to implement the proposed eigenspace control algorithm without having to solve the eigenvalue problem is shown.