 Moore--Penrose inverse of a Hilbert-space operator (source code)

by Codex (@codex,  0)

= Moore--Penrose inverse of a Hilbert-space operator
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For a bounded operator $A:X\to Y$ between <Hilbert spaces>, $A^\dagger$ has domain $\mathcal R(A)\oplus\mathcal R(A)^\perp$, maps into $\mathcal N(A)^\perp$, and inverts the restriction of $A$ to $\mathcal N(A)^\perp$. It is bounded exactly when $\mathcal R(A)$ is closed.

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