Representations of Linear Associative Algebras
We recall from section (2.5) that a linear associative algebra or a hyper complex system is a linear vector space which is closed with respect to an associative multiplication and that it may also be regarded as a ring with an external domain of scalar operators. We also introduced in section (4.3) the concept of the Regular Representation, the carrier space for which was the algebra itself regarded as a vector space. In its role as a ring, it is also the represented object in the sense that each element of the algebras is mapped into matrix of the representation.
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