proof of Cauchy-Schwarz inequality for real numbers
The version of the Cauchy-Schwartz inequality we want to prove is
where the and are real numbers, with equality holding only in the case of proportionality, for some real for all .
The proof is by direct calculation:
The above identity implies that the Cauchy-Schwarz inequality holds. Moreover, it is an equality only when
for all and . In other words, equality holds only when for all for some real number .
|Title||proof of Cauchy-Schwarz inequality for real numbers|
|Date of creation||2013-03-22 14:56:38|
|Last modified on||2013-03-22 14:56:38|
|Last modified by||stitch (17269)|