sidering the matrix of coefficients of the highest-order differential operators of the equation. For elliptic partial differential equations this matrix is positive definite, which has decisive influence on the set of possible solutions of the equation in question.[68]The finite element method is an important numerical method to solve partial differential equations, widely applied in simulating complex physical systems. It attempts to approximate the solution to some equation by piecewise linear functions, where the pieces are chosen with respect to a sufficiently fine grid, which in turn can be recast as a matrix equation.[69]සම්භාවිතා සිද්ධාන්ත සහ සංඛ්‍යානය[සංස්කරණය]Two different Markov chains. The chart depicts the number of particles (of a total of 1000) in state "2". Both limiting values can be determined from the transition matrices, which are given by [.70.31]{\displaystyle {\begin{bmatrix}.7&0\\.3&1\end{bmatrix}}} (red) and [.7.