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...Matrix algebra ryan c daileda trinity university linear recall every transformation t rn rm has the form x ax where a is standard e n wedened multiplication to correspond composition of transformations in terms columns this given by ab b bp abp i are found applying warnings although many familiar algebraic properties there several notable dierences even though and ba may both be dened have same dimensions general for instance if then but we say that commute with each other it also possible nonzero more generally does not obey cancellation law ac...