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In mathematics, a pseudoscalar in a geometric algebra is the highest-grade basis element of the algebra. For example, in two dimensions there are two basis vectors, e1, e2 and the highest-grade basis element is e1e2 = e12.This element squares to -1 and commutes with all elements — behaving therefore like the imaginary scalar i in the complex numbers. It is these scalar-like properties which give rise to its name.
In physics, a pseudoscalar denotes a physical quantity analogous to scalar. The only difference is that under the parity transformation, pseudoscalars flip their signs while scalars do not.
