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Homework Help: Showing that two 4x4 matrices are similar

  1. Jul 26, 2010 #1
    1. The problem statement, all variables and given/known data

    Given two 4x4 Matrices
    A = [0 -1 1 1, -1 1 0 0, 0 0 -1 1, 0 0 0 0] B = [-0.5 -0.5 -0.5 -1.5, -0.5 1.5 0.5 -0.5, 0 0 -1 1, 0 0 0 0]

    I need to show that these two matrices are similar.


    2. Relevant equations
    A = SBS^-1
    which simplifies to AS = SB


    3. The attempt at a solution
    I understand that I need to find a non-singular invertible matrix S that satisfies the equation: AS = SB, but I have spent many hours trying to find out how to find this matrix for a 4x4 matrix. In the text and in many of the online help pages, there are only examples of 2x2 matrices that have a very obvious matrix. I have not learned eigenvalues or eigenvectors yet, and do not wish to use them unless there really is no other way to show similarity.

    Thanks for any responses, and I appreciate any help on this problem.
     
  2. jcsd
  3. Jul 26, 2010 #2

    radou

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    It's a matrix equation. Name the elements of the matrix S (i.e. sij), multiply the matrices in order to obtain a system of equations, and see what happens.
     
  4. Jul 26, 2010 #3

    lanedance

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    just carring on from radou, S is not unique, if S is a solution, then so is 2S, so you just need to demonstrate any matrix that works
     
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