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A METHOD FOR OBTAINING THE CHARACTERISTIC EQUATION OF A MATRIX AND COMPUTING THE ASSOCIATED MODAL COLUMNS* By HENRY E. FETTIS (Air Materiel Command) The method described below is a process by which the characteristic equation of a matrix may be established without resorting to direct expansion of the coefficients by minors. Further, once the roots of the characteristic equation have been found, the corresponding eigenvectors can be found directly without the additional labor of solving a set of simultaneous equations. Since the only operations involved in the process are the standard ones of matrix multiplication and addition, the work can be set down and performed in routine fashion. The process may also be adapted to punch-card methods for matrices of large order. 1. Preliminary considerations. Consider the matrix

A method for obtaining the characteristic equation of a matrix and computing the associated modal columns