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Solving Linear Systems with Singular Matrices

Good morning! For (say, homogenous) linear systems of the form $$x_{n+1} = A x_n,$$ where $A$ is a nonsingular matrix, each initial value problem can be solved by the method of finding a general ...
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In which cases iterative equations can be reduced to finite-difference equations?

In which cases iterative equations can be reduced to finite-difference equations and when they can't?