Farkas' lemma

Summary

Farkas' lemma is a theorem^[1]. It draws 134 Wikipedia views per month (theorem category, ranking #173 of 1,306).^[2]

Key Facts

• Farkas' lemma's image is recorded as Farkas-generalise-wp.jpg^[3].
• Farkas' lemma's instance of is recorded as theorem^[4].
• Gyula Farkas is named after Farkas' lemma^[5].
• Farkas' lemma's has use is recorded as linear programming^[6].
• Farkas' lemma's Freebase ID is recorded as /m/07gy1f^[7].
• Farkas' lemma's defining formula is recorded as \begin{aligned} \forall A \in &\mathbb{R}^{m\times n}, \forall \mathbf{b} \in \mathbb{R}^n, \text{exactly one of the following is true:} \ &\begin{aligned} &\exists \mathbf{x} \in \mathbb{R}^n : \mathbf{Ax} = \mathbf{b} \land \mathbf{x} \geq 0 \ &\exists \mathbf{y} \in \mathbb{R}^{m} : \mathbf{A}^{\top}\mathbf{y} \geq 0 \land \mathbf{b}^{\top} \mathbf{y} < 0 \end{aligned} \end{aligned}^[8].
• Farkas' lemma's maintained by WikiProject is recorded as WikiProject Mathematics^[9].
• Farkas' lemma's Microsoft Academic ID is recorded as 27155235^[10].
• Farkas' lemma's in defining formula is recorded as \land^[11].
• Farkas' lemma's in defining formula is recorded as \mathbb R^n^[12].

Why It Matters

Farkas' lemma draws 134 Wikipedia views per month (theorem category, ranking #173 of 1,306).^[2] It has Wikipedia articles in 10 language editions, a strong signal of global cultural recognition.^[13]