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I read this statement and I would need some help with what it means:

If A is a matrix and $v$ is a vector such that $Av=0$ then there is a non-zero projection $P$ onto the subspace that annihilates $A$ on the right.

Does this mean that there is a $P$ such that $AP=0$?

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    Yes: but surely you need to assume that $\mathbf{v}\neq \mathbf{0}$? Also: are you translating or extracting this from some larger context? "onto **the** subspace" doesn't really make sense here: there is no subspace specified to which you can refer by the definite singular article.2011-09-27
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    You need $P^2=P$ as well.2011-09-27
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    @Arturo Magidin This is the exact version. You can have a look at it [here](http://mural.uv.es/rusanra/Lie%20Algebras%20in%20Particle%20Physics%202%C2%AA%20ed%20-%20From%20Isospin%20to%20Unified%20Theories%20(Georgi,%201999).pdf) (page 13)2011-09-27
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    @kuchnahi: You omitted a *lot* of context. You are working in the context of Schur's Lemma, with a particular pair of inequivalent irreducible representations of a group.2011-09-27
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    Turns out you are not right; "that annihilates $A$ on the right" does not refer to $P$, it refers to "subspace". You want the projection $P$ onto the subspace of all $\mathbf{w}$ such that $A\mathbf{w}=\mathbf{0}$.2011-09-27

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