Hölder's Inequality for Finite Sums/Euclidean Plane
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Hölder's Inequality for Sums: Euclidean Plane
In the context of a Euclidean plane, Hölder's Inequality for Sums takes the following form:
- $x_1 y_1 + x_2 y_2 \le \paren {\size {x_1}^p + \size {x_2}^p}^{1 / p} \paren {\size {y_1}^q + \size {y_2}^q}^{1 / q}$
where:
- $p, q > 1$
- $\dfrac 1 p + \dfrac 1 q = 1$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Hölder's inequality
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Hölder's inequality