MathDB
Miklos Schweitzer 1981_5

Source: convex cone in the n-dimensional real vector space

January 29, 2009
geometry3D geometryvectoradvanced fieldsadvanced fields unsolved

Problem Statement

Let K K be a convex cone in the n n-dimensional real vector space Rn \mathbb{R}^n, and consider the sets A\equal{}K \cup (\minus{}K) and B\equal{}(\mathbb{R}^n \setminus A) \cup \{ 0 \} (0 0 is the origin). Show that one can find two subspaces in Rn \mathbb{R}^n such that together they span Rn \mathbb{R}^n, and one of them lies in A A and the other lies in B B. J. Szucs
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