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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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$X \le V$, 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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