This preview shows page 1. Sign up to view the full content.
Unformatted text preview: .v/ D .v/ for v 2 V and 2 K . But this is immediate from the denition of the product, v C W D .v C W / . n V=W is called the quotient vector space and v 7! v C W the quotient map or quotient homomorphism . We have a homomorphism theorem for vector spaces that is analogous to, and in fact follows from, the homomorphism theorem for groups. Theorem 3.3.10. (Homomorphism theorem for vector spaces). Let T W V ! V be a surjective linear map of vector spaces with kernel N . Let W V ! V=N be the quotient map. There is linear isomorphism Q T W V=N ! V satisfying Q T D T . (See the following diagram.) V T q q q q q V q q q q q q q q q q q q = Q T V=N...
View
Full
Document
This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
 Fall '08
 EVERAGE
 Algebra, Multiplication, Scalar, Vector Space

Click to edit the document details