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Home arrow Extreme Directions
Extreme Directions

The property extreme direction arises naturally in connection with the pointed closed convex cone, being analogous to extreme point.  An extreme direction of a pointed closed convex cone is a vector corresponding to an edge that is a ray emanating from the origin.  In words, an extreme direction in a pointed closed convex cone is the direction of a ray, called an extreme ray, that cannot be expressed as a conic combination of any ray directions in the cone distinct from it.

    extreme directions

Extreme directions of the positive semidefinite cone, for example, are the rank-1 symmetric matrices.

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