Consider the following ket: |ψi> = c1|e1> + c2|e2>, where ci are some complex coefficients. Find the column-vector representation of |ψi> in the |ei> basis. Find the row-vector representation of <ψ| in the <ei| basis.
|ψi> = c1|e1> + c2|e2>
The Attempt at a Solution
Well I'm not sure what to do so I tried to start off by solving c1 and c2. To do this I multiplied |ψi> = c1|e1> + c2|e2> by <e1| to get that c1 = <e1|ψ> . Multiplying the same equation by <e2| gives c2 = <e2|ψ>
So I wrote |ψ> = <e1|ψ|e1> + <e2|ψ|e2>
Now I'm not sure what to do