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We use vector space projection (VSP) methods to design wide-band adaptive and self-healing arrays. Rectangular arrays are assumed but the VSP algorithm can be applied to any configuration. In the VSP method, we formulate a set of design constraints and then iteratively improve on a trial solution by operations known as "alternating projections". When all of the constraint sets are convex and the intersection of these sets is not the empty set, we can meet the design specifications in a finite dimensional setting. In our simulations, we show that reasonable design constraints are readily met. We demonstrate that VSP is useful for broad-band self-healing, i.e., the reconfiguration of the array when some broad-band elements fail to operate. Finally we compare our results with a known design procedure for broadband antenna arrays.