Therefore, it can not be unequivocally assumed that the conjugated vector will behave similarly to the native form.
2.
If is a real Lie algebra and is a representation of it over the vector space, then the conjugate representation } } is defined over the conjugate vector space } } as follows:
3.
An antilinear map f : V \ to W may be equivalently described in terms of the linear map \ bar f : V \ to \ bar W from V to the complex conjugate vector space \ bar W.
4.
More concretely, the complex conjugate vector space is the same underlying " real " vector space ( same set of points, same vector addition and real scalar multiplication ) with the conjugate linear complex structure " J " ( different multiplication by " i " ).
5.
A "'real structure "'on a complex vector space " V ", that is an antilinear involution \ sigma : V \ to V \,, may be equivalently described in terms of the linear map \ hat \ sigma : V \ to \ bar V \, from the vector space V \, to the complex conjugate vector space \ bar V \, defined by
मोबाइल