1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Showing a composition is isomorphic

  1. Oct 21, 2012 #1
    Prove that if S: U-->V and T: V-->W are isomorphisms, then TS (composition) is also an isomorphism.

    Idea: So my idea was since both S, T are both isomorphic that means they both have inverses S-1 and T-1. Now this is where I'm a little grey, in order to show that TS is isomorphic, is it enough for me to obtain the identity transformation "I" by multiplying the composition TS through by S-1T-1, based on the properties of linearity?

    TS = S-1T-1(TS) = S-1S = I ? or would I have to show the existence of (TS)-1? and if so how?
  2. jcsd
  3. Oct 21, 2012 #2
    I would just go through and show that TS satisfies the axioms. For example, [itex]TS(u_1+u_2) = T(S(u_1)+S(u_2))[/itex] and so on. BTW, what are V and W?
  4. Oct 21, 2012 #3

    Thanks. V and W are vector spaces
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook