When is $(A+B)^{\dagger}=A^{\dagger}+B^{\dagger}$ ?

preprint2020arXivOpen access

We address the question as to when it is true that $(A+B)^{\dagger}=A^{\dagger}+B^{\dagger},$ where $\dagger$ denotes the Moore-Penrose inverse. A similar question is addressed for the group inverse.

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When is $(A+B)^{\dagger}=A^{\dagger}+B^{\dagger}$ ?

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When is (A+B)†=A†+B†(A+B)^{\dagger}=A^{\dagger}+B^{\dagger}(A+B)†=A†+B†?

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When is $(A+B)^{\dagger}=A^{\dagger}+B^{\dagger}$ ?