Last Updated：2025/11/22

(linear algebra) Relative to a set S in Rⁿ, the set of points y such that the inner product of x and y is not positive for any point x in S.

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polar cone

Source Word

polar cone

Noun

(linear algebra) Relative to a set S in Rⁿ, the set of points y such that the inner product of x and y is not positive for any point x in S.

Japanese Meaning

線形代数学において、実数空間Rⁿ内の集合Sに対し、任意の点x ∈ Sとの内積が正でないすべての点yの集合を指す。

Sの極錐は、R^nに属するベクトルyのうち、Sの任意のxとの内積が非正になるもの全体である。

Sense（1）

(linear algebra) Relative to a set S in Rⁿ, the set of points y such that the inner product of x and y is not positive for any point x in S.

Since a is in S and b is in Sᵒ — the polar cone of S — we know that aᵀ b ≤ 0.

polar cones

（ plural ）