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February 27th, 2011, 12:47 PM  #1 
Newbie Joined: Feb 2011 Posts: 10 Thanks: 0  Kernel of a linear map over a vector space k
Hi Let be a linear map over a vector space where is generated by and where Also, for each Show that is nonzero. Please give me just a hint. 
February 27th, 2011, 01:50 PM  #2  
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7  Re: Kernel of a linear map over a vector space k Quote:
 
February 27th, 2011, 02:00 PM  #3 
Newbie Joined: Feb 2011 Posts: 10 Thanks: 0  Re: Kernel of a linear map over a vector space k is a linear map on a vector space M with for some is a field is algebra generated by satisfy the relation 
February 27th, 2011, 02:01 PM  #4 
Newbie Joined: Feb 2011 Posts: 10 Thanks: 0  Re: Kernel of a linear map over a vector space k
Thanx in advance

February 27th, 2011, 03:02 PM  #5 
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5  Re: Kernel of a linear map over a vector space k
Hi Saba, your notaion is confusing. Infact you keep changing it. The good thing is that you don't need anything of the algebra stuff for your result: Any nilpotent endomorphism f (i.e. ) of a nonzero vector space (or basically any structure you can think of) has this property. As a hint: Show the stronger result: The composition of any two injective morphisms is injective. Generalise to n morphisms and conclude your claim. 
February 27th, 2011, 03:08 PM  #6 
Newbie Joined: Feb 2011 Posts: 10 Thanks: 0  Re: Kernel of a linear map over a vector space k
if the map is injective , then ker(f) =0 But here ,show that ker f is NONzero 
February 28th, 2011, 03:27 AM  #7  
Senior Member Joined: Sep 2008 Posts: 150 Thanks: 5  Re: Kernel of a linear map over a vector space k Quote:
 

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kernel, linear, map, space, vector 
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