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I have recently encountered a symbol I don't recognize which has to do with linear algebra.

It is $X^o$. What does this mean?

(And just to be sure, $X\leq V$ means $X$ is a subset of $V$, right? What is the difference does this have with $\subseteq$?)

Thanks

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"I have recently encountered a symbol I don't recognize" - where? –  J. M. Nov 19 '11 at 11:18
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I'll be very surprised if the book/article/website/other you're reading doesn't define this notation on a previous page. –  Chris Taylor Nov 19 '11 at 11:41
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closed as not a real question by Jonas Meyer, Asaf Karagila, t.b., J. M., Zev Chonoles Dec 7 '11 at 4:56

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3 Answers

up vote 2 down vote accepted

$X \le V$, in the context of vector spaces, means that $X$ is a subspace of $V$, not just a subset.

$X^0$ probably means the annihilator of $X$: that is, the subspace of the dual $V*$ consisting of the linear functionals $f$ such that $f(x)=0$ for every $x$ in $X$.

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I think, $X^0$ is the space $Y$ which satisfied that $y\in Y,yX=0$.

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If $X$ is merely a subset of $V$, it could be the polar of $X$.

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