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As part of a course, I've been asked to write a map $C\rightarrow H,z \rightarrow zv$ for $v \in H=C^3\otimes C^2$, $v=[1, 0, 0, 1, 0, 1]$ in bra-ket notation.
However, I never written such a map before, and must have missed the lecture. I would very much appreciate if someone show me some example of how to write this kind of thing.
This map takes a complex number and returns a ket vector. In your case, this would simply mean writing $f(z) = z | v \rangle$.
Maybe a part of the exercise is to decipher $v$, then I would also expand it in ket notation: $| v \rangle = |0 \rangle \otimes |0 \rangle + |1\rangle \otimes |0 \rangle + |2\rangle \otimes |1 \rangle$.
It is somewhat tricky at first to think about vectors as maps from complex numbers to the vector space. If you want to describe a linear map $\mathbb{C} \rightarrow H$, then it's sufficient to specify $f(1)$, which is $v$.
