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Given rectangular matrices $A$ and $B$ so that $A \cdot B$ is well-defined, can we bound $\| (AB)^\dagger \|$ in terms of $\| A^\dagger \|$ and $\| B^\dagger \|$? Here, $A^\dagger$ and $B^\dagger$ are the pseudo-inverse matrices of $A$ and $B$, respectively.

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    my guess $\| (AB)^\dagger \| \leq \| A^\dagger \| \| B^\dagger \|$2012-07-18

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