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Suppose I have a vector $v$ in the complex space $\mathbb{C}^N$ with only a single non-zero element. Is there a standard notation to replace the vector with a scalar equal to the non-zero value of the vector?

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After some thought, I think $v\cdot e_i$ would suffice for this purpose, assuming the index i containing the non-zero element is known. But what if the index is unknown?

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You can use the dot product with the vector $(1, \dots, 1)^T$.

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  • $\begingroup$ That's so simple and it works! Thanks! $\endgroup$ – Paul Oct 16 '14 at 15:11
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I do not think so. Why not use $$ s \, e_k =<v,e_k>\,e_k $$ with a canonical vector $(e_k)_i = \delta_{ki}$.

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