November 10th, 2010, 07:02 AM  #1 
Member Joined: Sep 2007 Posts: 49 Thanks: 0  Isomorphism
This is a true/false question: All linear transformations from P3 to R2*2 are isomorphisms. I think it is true because dim(P3)=dim(R2*2)=4, and ker(P3)=0. But the answer was false. I don't know why...So that means kernel is not 0?? But P3 has to be zero in order for R2*2 to be 0.... Thanks. 
November 10th, 2010, 08:31 AM  #2 
Newbie Joined: Nov 2010 Posts: 3 Thanks: 0  Re: Isomorphism
It is false. If are vector spaces with , then is a linear transformation but it is not injective.  http://www.fernandorevilla.es/ 

Tags 
isomorphism 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Isomorphism  mathbalarka  Abstract Algebra  2  November 4th, 2012 10:53 PM 
isomorphism  tiger4  Abstract Algebra  2  July 2nd, 2012 02:17 AM 
Isomorphism  bewade123  Abstract Algebra  2  February 14th, 2012 04:12 PM 
Isomorphism  jpav  Abstract Algebra  6  July 11th, 2011 06:00 AM 
Isomorphism  just17b  Abstract Algebra  4  December 18th, 2007 07:57 AM 