I am working on inverse matrices and I have raised a problem about the inverse of the sum of two matrix. I have searched for quite a while but still could not find an answer. Does anyone know what is $(A+B)^{-1}$? Is it just $A^{-1} + B^{-1}$ or something else?
2026-04-03 21:02:22.1775250142
Equivalent of $(A+B)^{-1}$.
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Note that the sum can be non-invertible for instance $A=I$ and $B=-I$.
Assuming that's not the case there is The woodbury matrix identity