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Exterior algebra
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=== Projective geometry === Decomposable {{math|''k''}}-vectors in <math>{\textstyle\bigwedge}^{\!k}(V)</math> correspond to weighted {{Math|''k''}}-dimensional [[linear subspace]]s of {{tmath|V}}. In particular, the [[Grassmannian]] of {{math|''k''}}-dimensional subspaces of {{tmath|V}}, denoted {{tmath|\operatorname{Gr}_k(V)}}, can be naturally identified with an [[algebraic variety|algebraic subvariety]] of the [[projective space]] {{nowrap|<math display=inline>\mathbf{P}\bigl({\textstyle\bigwedge}^{\!k}(V)\bigr)</math>}}. This is called the [[Plücker embedding]], and the image of the embedding can be characterized by the [[Plücker relations]].
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