generated from smyalygames/quartz
11 lines
438 B
Markdown
11 lines
438 B
Markdown
# Definition
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$$(\cdot | \cdot) : V \times V \to \mathbb{C}$$
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> [!info]
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> $$V \times V \ni (u, v) \mapsto (u | v) \in \mathbb{C}$$
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> Such that $(au + bv | w) = a(u | w) + b(v|w)$
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> and $\overline{(u | v)} = (v | u)$
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> >[!example]-
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> > $$(w | au + bv) = \overline{(au + bv | w)} = \overline{a(u | w) + b (v | w)} = \bar{a} \overline{(u | w)} + \bar{b} \overline{( v | w)} = \dots$$
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>
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> and $(v | v) \geq 0$ and $(u | u) = 0 \implies u = 0$
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