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  "body": "\n## Summary\n\nA convex cone is a subset of a real vector space that is closed under addition and under multiplication by positive scalars.\nIt is the same as a set that is both a cone and [[convex|02AS45T3H9]].\nConvex cones describe the solution sets of homogeneous linear inequalities, orders on vector spaces, and the feasible regions of conic optimisation.\nExamples are the nonnegative orthant and the cone of positive semidefinite matrices.\n\n## Explanations\n\n### L1 human\n\nPicture a wedge or an ice cream cone with its tip at the origin, extending forever.\nIf two vectors lie in the wedge, so does their sum, and so does any stretched copy of one of them.\nThe first quadrant $\\set{(x, y) : x \\ge 0, y \\ge 0}$ of the plane is a convex cone.\nThe union of the first and third quadrants is not, because $(1, 0) + (0, -1) = (1, -1)$ falls outside.\n",
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