See Also: cauda nuclei caudati(medicine)
Cauchy-Schwarz inequality(encyclopedia)
corpus nuclei caudati(medicine)
caput nuclei caudati(medicine)
Schwarz(dictionary)
Cauchy(dictionary)
Dische-Schwarz reagent(medicine)
Cauchy, Augustin-Louis, Baron(encyclopedia)
rami caudati(medicine)
arteria lobi caudati(medicine)

Cauchy-Schwarz inequality (sh) and cauda nuclei caudati (medicine)


Cauchy-Schwarz inequality (sh)




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, (¡Òfg)2/n¡Ü/n(¡Òf2)(¡Òg2). 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, (¦²(ai, bi))2 ¡Ü ¦²(ai)2¦²(bi)2. In addition to functional analysis, these inequalities have important applications in statistics and probability theory.


cauda nuclei caudati (medicine)


cauda nuclei caudati -->
tail of caudate nucleus


The elongated posterior extension of the caudate nucleus that parallels the body and inferior horn of the lateral ventricle.

Synonym: cauda nuclei caudati, cauda striati.