Then in such a space the Cauchy-Schwarz inequality holds:
for any . That is, the modulus (since it might as well be a complex number) of the inner product for two given vectors is less or equal than the product of their norms. Equality happens if and only if the two vectors are linearly dependent.
If and the Cauchy-Schwarz inequality becomes
Cauchy-Schwarz inequality is also a special case of Hölder inequality. The inequality arises in lot of fields, so it is known under several other names as Bunyakovsky inequality or Kantorovich inequality. Another form that arises often is Cauchy-Schwartz inequality but this is a misspelling since the inequality is named after http://www-groups.dcs.st-and.ac.uk/ history/Mathematicians/Schwarz.htmlHermann Amandus Schwarz (1843–1921).
|Date of creation||2013-03-22 12:14:46|
|Last modified on||2013-03-22 12:14:46|
|Last modified by||drini (3)|