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=Isomorphisms - Brief Description and Application= | =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. | ||
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| + | The definition follows: | ||
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| + | " | ||
| + | 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.) | ||
[[ MA265Fall2010Momin|Back to MA265Fall2010Momin]] | [[ MA265Fall2010Momin|Back to MA265Fall2010Momin]] | ||
Revision as of 16:14, 6 May 2011
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.)
