When I was studying general relativity, I learned that to change a vector into a covector (or vice versa), one used the metric tensor. When I started quantum mechanics, I learned that the difference between a vector in Hilbert space and its dual is that each element of one is the complex conjugate of the corresponding element of the other.(adsbygoogle = window.adsbygoogle || []).push({});

Is there a metric tensor for Hilbert space that will do this - that is - change a vector into its dual, in the same way?

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# Hilbert space metric tensor?

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