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seen Jul 9 at 21:18

Jul
3
comment Proof that a linear transformation is isomorphic
@Andrea Mori: I must confess that i have some problems to understand the current contents of our lecture, but give me a try. For every linear transformation $T$ from one space $X$ to anothe one called $Y$ with dim$X$=dim$Y$ i can say that $T$ is isomorphic, when i proove bijection. Let $T$ be injective and therefore the kernel is trivial. Due to the rank–nullity theorem we have dim im T = dim X - dim ker T = dim Y and $T$ is bijective if dim im T = dim Y, that means im $T = Y$. However $T$ is surjective if im $T = Y$ what has been proven. -> Therefore $T$ is isomorphic. / Is that ok?
Jul
3
comment Proof that a linear transformation is isomorphic
I am sorry, but i do not understand what you want to express with that (trivial) implication.
Jul
2
comment Negative 1 to the power of Infinity
Thanks for the precise answer - helped me out! (I will accept this as the solution when i am allowed in about 5 minutes)