1. Not finding help here? Sign up for a free 30min 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!

Isomorphism: matrix determinant

  1. Jan 19, 2009 #1
    Determine whether the given map [tex]\varphi[/tex] is an isomorphism of the first binary structure with the second.
    < M2(R ), usual multiplication > with <R, usual multiplication> where [tex]\varphi[/tex](A) is the determinant of matrix A.

    The determinant of the matrix is ad-bc, so [tex]\varphi[/tex](A)=ad-bc.
    For this to be an isomorphism, I have to show that the function is one to one, onto and preserves the operations.
    I'm having trouble getting this to work. Any suggestions?
     
  2. jcsd
  3. Jan 19, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Maybe it can't....
     
  4. Jan 19, 2009 #3
    According to the book it is suppose to be an isomorphism, the question says it is. I can get it to be one to one and onto, but i am having trouble with it preserving the operations.
     
  5. Jan 19, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You just said that you must prove the function is "one to one". That is that two different matrices, such as
    [tex]\begin{bmatrix}2 & 1 \\ 1 & 1\end{bmatrix}[/tex]
    and
    [tex]\begin{bmatrix}3 & 2\\ 1 & 1\end{bmatrix}[/tex]
    must not have the same determinant. Is that true?

    I think you should to reread that problem.
     
  6. Jan 19, 2009 #5

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No it doesn't. The question is asking you whether or not it is.
     
  7. Jan 19, 2009 #6
    Oh duh... That was stupid... It doesn't have to be. Thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Isomorphism: matrix determinant
  1. Determine Matrix A (Replies: 1)

Loading...