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Change of Basis in 2D

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Given a point in the plane you can see its coordinates with respect to the standard basis , or compute its coordinates with respect to a different basis . The signed area of the parallelogram determined by this basis, , is a crucial quantity.

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This Demonstration complements the Demonstration "Coordinates of a Point Relative to a Basis in 2D", by E. Schulz, which shows how a point varies as its coordinates change.

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Contributed by: Adriano Pascoletti (March 2011)
Open content licensed under CC BY-NC-SA

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