Unit pseudoscalars Unit pseudoscalars are blades that play important roles in GA. A unit pseudoscalar for a non-degenerate subspace of is a blade that is the product of the members of an orthonormal basis for . It can be shown that if and are both unit pseudoscalars for , then and . If one doesn't choose an orthonormal basis for , then the Plücker embedding gives a vector in the exterior algebra but only up to scaling. Using the vector space isomorphism between the geometric algebra and exterior algebra, this gives the equivalence class of for all . Orthonormality gets rid of this ambiguity except for the signs above.
Unit pseudoscalars Unit pseudoscalars are blades that play important roles in GA. A unit pseudoscalar for a non-degenerate subspace of is a blade that is the product of the members of an orthonormal basis for . It can be shown that if and are both unit pseudoscalars for , then and . If one doesn't choose an orthonormal basis for , then the Plücker embedding gives a vector in the exte:rior algebra but only up to scaling. Using the vector space isomorphism between the geometric algebra and exterior algebra, this gives the equivalence class of for all . Orthonormality gets rid of this ambiguity except for the signs above.