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I'd like to know how one goes about finding a basis for the intersection of two subspaces V and W of a given vector space U. I am aware of the identity [tex]V \cap W = (V^{\per} \cup W^{\per})^{\per}[/tex] (essentially the orthogonal space of the union of orthogonal spaces of V and W), but this isn't computationally efficient. Furthermore it requires an inner product to be defined on U. Are there any other methods of computing a basis for [tex]V \cap W[/tex] if given bases for both V and W (methods that may not require conditions such as the one mentioned above)?

EDIT: My perpendicular symbols didn't show.

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# Algorithms for quantifying intersections of subspaces

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