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January 8th, 2013, 03:51 AM  #1 
Member Joined: May 2012 Posts: 56 Thanks: 0  Linear Transformations and Matrices
In the page that I attached, (for theorem 2.126) I was a bit confused about why . Also, for theorem 2.127, I was confused about . In order to show that something is a ring homomorphism, we need to show that F(1)=1, right? But I'm confused here, because aren't we supposed to say F(I) = I (since the identity matrix of V is I)? Why do they instead say . Isn't the identity map...then how is it the identity element? Thanks in advance 
January 8th, 2013, 06:28 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Linear Transformations and Matrices
Sorry but I see no attachment. The sum you give, makes no sense to me. I think it should be . For you second question, what distinction are you making between "1" and "I"? They are both commonly used for the multiplicative identity in an algebraic structure, such as ring.

January 8th, 2013, 08:36 AM  #3  
Member Joined: May 2012 Posts: 56 Thanks: 0  Re: Linear Transformations and Matrices Quote:
I'm sorry, I didn't realize that I didn't attach anything... Also, for ...I thought that meant the identity map, that's why I was confused. It makes sense now, since you said it was the identity element...but then why don't they just write F(I)=I?  

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