Ferguson's Theorem

Ferguson’s Theorem states that, under certain conditions, applying a linear transformation to a convex set (a smoothly curved, "bulging outward" shape) preserves the convexity of that set. In simpler terms, if you have a shape that is convex, and you transform it using a specific kind of linear operation, the resulting shape will still be convex. This is important in mathematical optimization and analysis because it guarantees that certain manipulations won't break the desirable property of convexity, helping to ensure problems remain solvable and well-behaved.