Cauchy–Schwarz inequality

Cauchy–Schwarz inequality

In mathematics, the Cauchy–Schwarz inequality, also known as the Schwarz inequality, the Cauchy inequality, or the Cauchy–Schwarz–Bunyakovsky inequality, is a useful inequality encountered in many different settings, such as linear algebra applied to vectors, in analysis applied to infinite series and integration of products, and in probability theory, applied to variances and covariances.

The inequality for sums was published by
*citation|first=A. |last=Cauchy|title= Oeuvres 2, III|page=373|year=1821
*citation|first=S. S. |last=Dragomir|title=A survey on Cauchy-Bunyakovsky-Schwarz type discrete inequalities|journal=JIPAM. J. Inequal. Pure Appl. Math.|volume=4|issue=3|year=2003|pages=142 pp|url=http://jipam.vu.edu.au/article.php?sid=301
*citation|first=R.V.|last= Kadison|title= A generalized Schwarz inequality and algebraic invariants for operator algebras|journal=Ann. of Math.|volume=56|year= 1952.
*citation|first=V. |last=Paulsen|title=Completely Bounded Maps and Operator Algebras|publisher= Cambridge University Press|year= 2003.
*citation|first=H. A. |last=Schwarz|year=1888 |pages=318|journal=Acta Societatis scientiarum Fennicae|volume=XV |title=Über ein Flächen kleinsten Flächeninhalts betreffendes Problem der Variationsrechnung|url=http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/Schwarz.pdf
*springer|title=Cauchy inequality|id=C/c020880|first=E.D. |last=Solomentsev
*citation|url=http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html |first=J.M. |last=Steele|title=The Cauchy–Schwarz Master Class|publisher= Cambridge University Press|year=2004|ISBN=052154677X


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  • Cauchy-Schwarz inequality — /koh shee shwawrts , koh shee shvahrts /, Math. See Schwarz inequality (def. 2). * * * Any of several related inequalities developed by Augustin Louis Cauchy and, later, Herman Schwarz (1843–1921). The inequalities arise from assigning a real… …   Universalium

  • Cauchy-Schwarz inequality — /koh shee shwawrts , koh shee shvahrts /, Math. See Schwarz inequality (def. 2) …   Useful english dictionary

  • Cauchy-Schwarz inequality — noun 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 …   Wiktionary

  • Cauchy's inequality — Math. See Schwarz inequality (def. 1). [named after A. L. CAUCHY] * * * …   Universalium

  • Cauchy's inequality — Math. See Schwarz inequality (def. 1). [named after A. L. CAUCHY] …   Useful english dictionary

  • Schwarz inequality — Math. 1. Also called Cauchy s inequality. the theorem that the inner product of two vectors is less than or equal to the product of the magnitudes of the vectors. 2. Also called Cauchy Schwarz inequality. the theorem that the square of the… …   Universalium

  • Schwarz inequality — Math. 1. Also called Cauchy s inequality. the theorem that the inner product of two vectors is less than or equal to the product of the magnitudes of the vectors. 2. Also called Cauchy Schwarz inequality. the theorem that the square of the… …   Useful english dictionary

  • Schwarz inequality — noun Cauchy Schwarz inequality …   Wiktionary

  • Cauchy-Schwarz-Abschätzung — Die Cauchy Schwarz Ungleichung, auch bekannt als schwarzsche Ungleichung oder Cauchy Bunjakowski Schwarz Ungleichung, ist eine nützliche Ungleichung, die in vielen Bereichen der Mathematik verwendet wird, z. B. in der Linearen Algebra (Vektoren) …   Deutsch Wikipedia

  • Cauchy-Schwarz-Ungleichung — Die Cauchy Schwarz Ungleichung, auch bekannt als schwarzsche Ungleichung oder Cauchy Bunjakowski Schwarz Ungleichung, ist eine nützliche Ungleichung, die in vielen Bereichen der Mathematik verwendet wird, z. B. in der Linearen Algebra (Vektoren) …   Deutsch Wikipedia

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