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Aug 8, 2013 at 5:11 comment added Tom LaGatta Definition: "A convex space (also called barycentric algebra and other terms, invented independently many times) is a set equipped with a notion of taking weighted averages, or convex-linear combinations, of its elements. Do not confuse this with an (abstract) convex set , which a special kind of convex space, also defined below." || mathoverflow.net/a/117138/238
Dec 25, 2012 at 13:44 comment added Konrad Waldorf @Joël: Good, I've tried to include it.
Dec 25, 2012 at 13:43 history edited Konrad Waldorf CC BY-SA 3.0
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Dec 24, 2012 at 21:35 comment added Joël @Konrad: yes, it helps. It helps even so much that I think you should incorporate this in your answer.
Dec 24, 2012 at 12:40 comment added Konrad Waldorf @Qiaochu Yuan: I see. Maybe it helps to emphasize that there is no addition at all on the set of states? It's just a convex set, not a vector space.
Dec 24, 2012 at 11:51 comment added Qiaochu Yuan This answer doesn't explicitly distinguish between two notions of superposition which come into play here, namely addition of vectors and addition of trace class operators, which could be confusing to the uninitiated.
Dec 24, 2012 at 11:13 history answered Konrad Waldorf CC BY-SA 3.0