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

cauchy schwarz inequality matrix | 1.88 | 0.2 | 7271 | 100 | 32 |

cauchy | 0.66 | 1 | 9594 | 58 | 6 |

schwarz | 1.82 | 0.9 | 3693 | 96 | 7 |

inequality | 0.58 | 0.9 | 5819 | 86 | 10 |

matrix | 0.69 | 0.8 | 9402 | 92 | 6 |

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

cauchy schwarz inequality matrix | 1.95 | 0.1 | 6802 | 70 |

cauchy schwarz inequality for matrix | 1.25 | 0.2 | 4580 | 76 |

cauchy schwarz inequality matrix inverse | 1.95 | 0.7 | 9051 | 10 |

cauchy schwarz inequality for matrices | 0.87 | 0.2 | 4646 | 37 |

The Cauchy-Schwarz inequality is one of the most widely used inequalities in mathematics, and will have occasion to use it in proofs. We can motivate the result by assuming that vectors u and v are in ℝ 2 or ℝ 3. In either case, 〈 u, v 〉 = ‖ u ‖ 2 ‖ v ‖ 2 cos θ.

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). )(c+a+b). ).

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).

As explained in class, if you believe that vectors in hundreds of dimensions act like the vectors you know and love in R2, then the Cauchy-Schwartz inequality is a consequence of the law of cosines. Speci cally, uv = jujjvjcos, and cos 1.