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Calculating Inner Products
The Prompt
For the generic bra vector $<v|$ and ket vector $|w>$ we can compute the inner product. Write it down.
With vectors
$$ \vert 1\rangle =\left(\begin{array}{c} 1\\ 0\\ 0\\ \end{array}\right) $$ $$ \vert r\rangle =\left(\begin{array}{c} 0\\ 1\\ 1\\ \end{array}\right) $$
Compute $\langle 1\vert r\rangle$ and $\langle r\vert 1\rangle$.
Compute $\langle v_{1}\vert v_{2}\rangle$ for eigenvectors
$$ \vert v_{1}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ 1\\ \end{array}\right) $$
$$ \vert v_{2}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c} 1\\ -1\\ \end{array}\right) $$
Context
This SWBQ
