The modify method of building minimum multitude of systems linear algebraic equations

The article provides modified method of constructing the minimal polynomial using solving systems of linear algebraic equations. proposed approach , without changing the basic idea of the method enables the highest power to reduce the number of calculations. If earlier to build coefficients of the minimal polynomial of the matrix $ n $ - th order with using the method it was necessary to seek the solution of linear systems algebraic equations of order $n^2\times m$, $n<m$, then modified method it is enough to look for the solution of systems of linear algebraic equations of order $n\times m$, $n<m$