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January 8th, 2013, 03:51 AM   #1
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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
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January 8th, 2013, 06:28 AM   #2
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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.
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January 8th, 2013, 08:36 AM   #3
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Re: Linear Transformations and Matrices

Quote:
Originally Posted by HallsofIvy
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.
Thanks for answering,

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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