Isomorphisms - Brief Description and Application
This topic is covered in section 4.8 of textbook for MA265. The basic idea of isomorphism has to do with structures that while appearing different are structurally the same.
The definition follows:
" Let V be a real vector space with operations + (addition) and *(scalar multiplication) and let W be a real vector space with operations + (addition) and *(scalar multiplication). A one-to-one function L mapping V onto W is called isomorphism (from the Greek isos meaning "the same" and morphos meaning structure) of V onto W if:
a) L(v+w)=L(v)+L(w) for v, w in V b) L(c*v)=c*L(v) for v in V, c is a real number "
(Elementary Linear Algebra with Applications, Kolman and Hill, 9th ed.)
