Jordan algebras in R

A Jordan algebra is a non-associative algebra over the reals with a bilinear multiplication that satisfies the following identities:

xy=yx

(xy)(xx)=x(y(xx))

(the second identity is known as the Jordan identity). In literature one usually indicates multiplication by juxtaposition but one sometimes sees . Package idiom is to use an asterisk, as in x*y. There are five types of Jordan algebras, all of which have their own representation in the package, which uses S4 methods.

Further information

For more detail, see the package vignette

vignette("jordan")