# How to write the map $\mathbb C\ni z\mapsto zv$ in bra-ket notation?

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.

• you can find explanations of braket notation in here and links therein. Could you spell out what specifically (if anything) you find unclear in what is said there?
– glS
Feb 26 '19 at 20:11

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 $$v$$.