cauchy-schwarz inequality

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Cauchy-Schwarz inequality

A theorem which states that the absolute value of the dot product between two vectors is less than or equal to the product of the magnitudes of the two vectors

Cauchy-Schwarz inequality

Any of several related inequalities developed by Augustin-Louis Cauchy and, later, Herman Schwarz (1843-1921). The inequalities arise from assigning a real number measurement, or norm, to the functions, vectors, or integrals within a particular space in order to analyze their relationship. For functions f and g, whose squares are integrable and thus usable as a norm, (fg)^2/n/n(f^2)(g^2). For vectors a = (a1, a2, a3,..., an) and b = (b1, b2, b3,..., bn), together with the inner product (see inner product space) for a norm, ((ai, bi))^2 (ai)^2(bi)^2. In addition to functional analysis, these inequalities have important applications in statistics and probability theory

Cauchy-Schwarz inequality.

Schwarz inequality

Heceleme

cauchy-schwarz in-e-qua-li-ty

Etimoloji

() Named after Augustin-Louis Cauchy|Augustin-Louis Cauchy]] and Hermann Amandus Schwarz|Hermann Amandus Schwarz]].