Is the basis vector ##(i,0,1)## in the space ##V=##Span##((i,0,1))## with a standard inner product,over ##\mathbb{C}^3##(adsbygoogle = window.adsbygoogle || []).push({});

orthogonal to itself?

##<(i,0,1),(i,0,1)> = i \cdot i + 0 \cdot 0 + 1 \cdot 1 = -1 + 1 = 0 ##

The inner product (namely dot product) of this vector with itself is equal to zero.

What is going on here?

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# Is this complex vector orthogonal to itself?

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