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...C macduffee matrices of an algebra we may also write conditions in the form k whence it follows that aid j ne x n where a are define first matrix r by equation ri rn and second s aisi thus is isomorphic with if only i linearly independent l su two invariants apply to basal numbers eu e linear transformation f yaa coefficients gf constants multiplication subject induced o lj si ij jarpdsqcpqjy t z wj p q this be written acisr rtaipcpqtdsqy for example see transactions society vol hence while drop primes now have cij associativity jcijkcjcsr cihrcj sk consider those equations which w pass obtaining cijkrk since djk set composed all readily from so invariant zero subalgebra has additional property...