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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.**


{{swbq:prsw:prswinner1.ppt|Powerpoint slide}}
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{{swbq:prsw:prswinner1.pdf|PDF slide}}


**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** $\langle r\vert 1\rangle$**.**

{{swbq:prsw:prswinner2.ppt|Powerpoint slide}}
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{{swbq:prsw:prswinner2.pdf|PDF slide}}

**Compute** $\langle v_{1}\vert  v_{2}\rangle$ **for eigenvectors**

$$
\vert v_{1}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c}
1\\
1\\ \end{array}\right)
$$

$$
\vert v_{2}\rangle=\frac{1}{\sqrt{2}}\left(\begin{array}{c}
1\\
-1\\ \end{array}\right)
$$

{{swbq:prsw:prswinner3.ppt|Powerpoint slide}}
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{{swbq:prsw:prswinner3.pdf|PDF slide}}

===== Context =====

This [[strategy:smallwhiteboard:|SWBQ]]

===== Wrap Up =====

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