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This correspondence identifies general conditions under which the generalized sidelobe canceller (GSC) structure implements a linearly constrained minimum variance (LCMV) broad-band beam-former. In previously published work, conditions have been presented for the case in which the linear constraint is restricted to fixed gain in the steer direction. Here, that work is extended to include general linear constraints. A geometric interpretation is presented to provide insight into the relationship between the GSC structure and LCMV beamformers, and several recent developments in broad-band beam-forming are reviewed and related to the GSC structure.