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with all nonnegative components (x_i >= 0 and y_i >= 0 for all : in the first quadrant if 2-dimensional, in the first octant if 3-dimensional), then for each pair of components x_i and y_i one of the pair must be zero, hence the name complementarity. e.g. X = (1, 0) and Y = (0, 2) are complementary, but X = (1, 1) and Y = (2, 0) are

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