My Math Forum Convex combination

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 June 22nd, 2012, 09:24 AM #1 Senior Member   Joined: Apr 2012 Posts: 106 Thanks: 0 Convex combination Hi, I need to find such A and B so that the following statement will be true $Conv(A) \cup Conv(B) \ne Conv (A \cup B)$ I would be thankful for any advice on this.
 June 22nd, 2012, 12:29 PM #2 Global Moderator   Joined: May 2007 Posts: 6,755 Thanks: 695 Re: Convex combination Simple example (2 dimension): A = {(-1,0),(1,0)}, B = {(0,-1),(0,1)}. Conv(A) is interval from -1 to 1 along x axis, Conv(B) is interval from -1 to 1 along y axis, Conv(A?B) is diamond shaped object with corners at the points of A and B. Conv(A)?Conv(B) is just the union of the two intervals.

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