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## Homework Statement

I was discussing the proof for the Cauchy-Schwarz inequality used in our lectures, and another student suggested an easier way of doing it. It's really, really simple. But I haven't seen it anywhere online or in textbooks, so I'm wondering if it's either wrong or is only valid in certain scenarios.

The quick version is this:

[itex]u \bullet v = ||u|| ||v|| cosθ[/itex] where θ is between 0 and [itex]\pi[/itex].

The upper and lower bounds of |cosθ| are 1 and 0, respectively, so [itex]|u \bullet v | \leq ||u|| ||v||[/itex]