In mathematics, the Cauchy–Schwarz inequality (also known as the Bunyakovsky inequality, the Schwarz inequality, or the Cauchy–Bunyakovsky–Schwarz inequality), is a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, and other areas. It is considered to be one of the most important inequalities in all of mathematics. It has a number of generalizations, among them Hölder's inequality.