 #1
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Equation 9.2.25 defines the inner product of two vectors in terms of their components in the same basis.
In equation 9.2.32, the basis of ## V \rangle## is not given.
## 1 \rangle ## and ## 2 \rangle ## themselves form basis vectors. Then how can one calculate ## \langle 1 V \rangle ## ?
Do we have to assume that all of these vectors are given in the orthogonal basis with vectors given by
## \begin{bmatrix}
1
\\ 0
\end{bmatrix} ## and ## \begin{bmatrix}
0
\\ 1
\end{bmatrix} ## ?
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