Abstract-This paper presents the theoretical framework for a new technique in the field of linear antenna arrays with amplitude control called error coefficient matrix. First of all, the array factor is expressed as a summation of contribution from the elements of the array. It will be shown that for small errors in excitation amplitude, the error in the overall radiation pattern at a given angle is a summation of errors contributed by the individual elements of the array at that angle. An error coefficient matrix is proposed, and its properties are discussed in great detail. The accuracy of the proposed method is investigated for varying levels of errors in weights and for varying number of error elements, using Monte-Carlo simulation. Finally, the applications of this new technique in the field of antenna arrays are presented.