What do the single bars in the Cauchy-Schwarz equation represent?

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I need to write out the proof for the Cauchy-Schwarz equation from quantum computing. I'm stuck on the first step as I don't understand what the single bars on the first term in the equation. Double bars is length but single??


http://en.wikipedia.org/wiki/Cauchy–Schwarz_inequality
 
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Single bars indicate the absolute value, or magnitude.

For the record, it's not uncommon for people to use single bars to designate the norm (length) of a vector, even though the proper notation is technically double bars.
 
Thanks I was totally stuck, as in all the notes the professor used double bars.