Keyword | CPC | PCC | Volume | Score | Length of keyword |
---|---|---|---|---|---|

cauchy schwarz inequality complex | 0.26 | 1 | 1088 | 34 | 33 |

cauchy | 0.01 | 0.3 | 2959 | 38 | 6 |

schwarz | 0.89 | 0.4 | 2346 | 84 | 7 |

inequality | 0.54 | 0.7 | 2582 | 91 | 10 |

complex | 0.25 | 0.6 | 8299 | 32 | 7 |

Keyword | CPC | PCC | Volume | Score |
---|---|---|---|---|

cauchy schwarz inequality complex | 1.86 | 1 | 2556 | 7 |

Cauchy-Schwarz Inequality The Cauchy-Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, states that for all sequences of real numbers

Proving the Schwarz Inequality for Complex Numbers using Induction 11 Rudin Theorem 1.35 - Cauchy Schwarz Inequality 2 Complex number condition on the modulus 0 Prove Basic Complex Number Inequalities

At first glance, it is not clear how we can apply Cauchy-Schwarz, as there are no squares that we can use. Furthermore, the RHS is not a perfect square. The power of Cauchy-Schwarz is that it is extremely versatile, and the right choice of can simplify the problem. ( a c × c + b a × a + c b × b) 2 ≤ ( a 2 c + b 2 a + c 2 b) ( c + a + b).

"A Generalized Schwarz Inequality and Algebraic Invariants for Operator Algebras". Annals of Mathematics. 56 (3): 494–503. doi: 10.2307/1969657. JSTOR 1969657. ^ Paulsen, Vern (2002). Completely Bounded Maps and Operator Algebras. Cambridge Studies in Advanced Mathematics. 78. Cambridge University Press. p. 40. ISBN 9780521816694.