Cauchy's Inequality/Also presented as

Cauchy's Inequality: Also presented as

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

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

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