March 17th, 2017, 08:27 AM  #1 
Senior Member Joined: Aug 2014 From: United States Posts: 137 Thanks: 21 Math Focus: Learning  dual vector space
I know that $(V^*)^*\cong_{vec} V$ for finite dimensional vector spaces $V$. However, it also seems as if $V\cong_{vec} V^*$, since for finite dimension, $V$ and $V^*$ are both vector spaces of the same dimension, and any two vector spaces of the same finite dimension are isomorphic. But I know that $V$ and $V^*$ are not isomorphic as vector spaces, so what's wrong with my above logic? 
March 17th, 2017, 10:09 AM  #2 
Senior Member Joined: Aug 2012 Posts: 1,960 Thanks: 547  

Tags 
dual, space, vector 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Dual Vector Space  mathftw  Linear Algebra  1  March 17th, 2016 03:57 AM 
Is a vector space's sub space a vector system?  Meph  Linear Algebra  3  November 12th, 2015 09:19 AM 
practice question integrating polynomial  dual vector space  vascosca  Linear Algebra  2  February 15th, 2013 12:47 PM 
dual space bijection  cummings123  Linear Algebra  1  October 27th, 2012 08:23 AM 
vector space  ely_en  Abstract Algebra  6  January 8th, 2012 07:44 AM 