# polar cone

Definition from Wiktionary, the free dictionary

## English[edit]

### Noun[edit]

**polar cone** (*plural* **polar cones**)

- (linear algebra) Relative to a set
*S*in**R**^{n}, 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*S^{o}*— the*S**polar cone**of*— we know that*a^{T}b ≤ 0*.*

#### See also[edit]

- (set of points): dual cone

### References[edit]

- Vince A. Sposito and H. T. David, "A Note on Farkas Lemmas Over Cone Domains",
*SIAM Journal on Applied Mathematics*, Vol. 22, No. 3. (May, 1972), pp. 356-358. [1]