Vector Space of Linear Maps

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Definition of linear map. Algebraic properties of linear maps.
  1. Sheldon Axler
  2. linear algebra
  3. Linear Algebra Done Right
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Комментарии
Автор

OMG your explanation is the most complete and precise one can ever find. Thanks for summarizing your book in a series of precise definitions and examples! <3

briancannard
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Does anyone else find the problems extremely challenging? I have the illusion of understanding as I’m reading the chapter, but then completely struggle with the problems. And advice or input is welcome.

worththekeeping
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Another question. Assuming we have that (T : V->W), Is it required that T is defined for the whole of V? If I have a function like T : R->R where T(x)=3x but x is restricted to the interval (-3...3), then T(4) is undefined but by homogeneity you could rewrite this as T(2*2)=2T(2)=12
Or does the requirement depend on which choice of V you use maybe?

leugli
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7:40
Since T is the unique linear map for this case, does that mean that I can always just use the function given in the proof as a linear map such that T(vj)=wj?

leugli
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Is there any reason why integration goes from 0 to 1?, can be other limits?

pablomoreno