User talk:Thedarkleaf

Cauchy-Schwarz inequality

An alternate proof, which i learnt is as follows: cos x = u . v / ||u|| ||v|| as cos x is between -1 and 1, the absolute value of the denomenator must be larger or equal to the numerator, hence u . v <= ||u|| ||v|| TheDarkLeaf 17:30, 19 June 2005 (AEST)

But first you need to establish that the cosine does play that role. You can give an easy intuitive geometric argument, but whether it works in, e.g., infinite-dimensional spaces may be dubious. Michael Hardy 23:25, 19 Jun 2005 (UTC)

Oh, and notice this notation:

u · v ≤ ||u|| ||v||.

Also, notice the difference between the following:

between -1 and 1

between −1 and 1

A stubby little hyphen used as a minus sign is sometimes -- especially in subscripts and superscripts -- hard to see. Michael Hardy 23:27, 19 Jun 2005 (UTC)