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Hi.

If you have a differential equation [itex]\mathcal L y=f[/itex] where [itex]\mathcal L[/itex] is some linear differential operator, then you can find a particular solution using the Green's function technique. It is then said that the Green's function is kind of the inverse to [itex]\mathcal L[/itex], even though [itex]\mathcal L[/itex] might not really have an inverse. Is it possible to do something similar for matrices? I.e. if we have a matrix equation [itex]\mathbf Ax=b[/itex], is there some matrix that can give me a particular solution [itex]x=\mathbf Gb[/itex] even though [itex]\mathbf A[/itex] might not be invertible ?

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# Matrix Green's function

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