Linear algebra: The module of morphisms
In this chapter we continue our development of linear algebra. We study the module of morphisms, the module made from collecting together all the morphisms from one module to another. The coordinate morphism provides the tie between the module of morphisms and the module of m by n matrices. The collective structure of the module of morphisms is further extended through composition to produce the algebra of endomorphisms and the corresponding algebra of square matrices. Through the use of the matrix of a morphism and the coordinates of a vector we calculate the images of morphisms in the traditional way.
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