| The minimal polynomial of a matrix contains some very basic information on the matrix (e.g., spectral structure). Consequently, the minimal polynomial of a given matrix provides useful and important knowledge in analysing matrices that arise in applications. In practice, however, it is important to know not only the minimal polynomial itself but also the mechanism of obtaining the minimal polynomial. We present an algorithmic method for computing the minimal polynomial of any square matrix. Since the method uses basic operations, it is algebraically and theoretically simple to apply. The method allows us to compute the exact minimal polynomial of any reasonably small size matrix which is usually a complicated task in any conventional method for obtaining the minimal polynomial. In some cases, the simplicity of the method provides simple proofs of theorems in matrix analysis and reveals some desirable intrinsic properties of the matrix. |
