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 &middot; v &le; ||u|| ||v||.

Also, notice the difference between the following:


 * between -1 and 1
 * between &minus;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)