Cauchy's Inequality/Also presented as

Cauchy's Inequality: Also presented as

Cauchy's inequality can also be expressed in the form:

$\ds \sum_{i \mathop = 1}^n r_i s_i \le \sqrt {\paren {\sum_{i \mathop = 1}^n {r_i}^2} \paren {\sum_{i \mathop = 1}^n {s_i}^2} }$

where all of $r_i, s_i \in \R$.


Sources

  • 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Cauchy's inequality
  • 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Cauchy-Schwarz inequality for sums
  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Cauchy-Schwarz inequality for sums
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