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: Equivalent matrix?

  1. May 6, 2007 #1
    1. The problem statement, all variables and given/known data
    How do you turn the transformation matrix

    1+i 3
    2-i 5i

    into a diagonal matrix when it is transforming vectors in the Z module?

    What is the Z module? Normally one states R module M. where R is the coefficient one multiplies to the elements in the module.

    3. The attempt at a solution
    I have tried but can't seem to reduce to diagonal form as I can only multiply by integer numbers?
  2. jcsd
  3. May 6, 2007 #2
    I have just worked out the diagonal matrix. It is

    1 0
    0 8+11i

    However my question of what is the Z module still stands. I know clearly what a Z ring is.
  4. May 6, 2007 #3


    User Avatar
    Science Advisor

    Z is the same whether you think of it as a ring or a module- the "Gaussian integers"- all numbers of the form a+ bi where a and b are integers and i is, of course, the imaginary unit.
  5. May 6, 2007 #4
    I think that the Z module is refering to any module where the coefficients are from the ring of the Gaussian integers. Why use the word Gaussian?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook