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Similar matrices

  1. Mar 21, 2010 #1
    If A and B are similar matrices, then show that A-xI and B-xI are similar were x is a scalar.

    How to start?
  2. jcsd
  3. Mar 21, 2010 #2


    Staff: Mentor

    Since A and B are similar, you know that A = P-1BP.

    Then A - xI = P-1BP - xI = P-1BP -Ix. (You can multiply by a constant on the right or the left).

    If you work with this maybe you can end up with what you need to show that A - xI is similar to B - xI.
  4. Mar 21, 2010 #3
    If we have this line A - xI = P-1BP - xI, can't I just add xI from the left to right?
  5. Mar 21, 2010 #4


    Staff: Mentor

    I'm not sure what you're asking. xI and Ix are equal. In general, cA = Ac, where c is a scalar and A is a matrix.

    I wrote it the way I did for a reason, though.
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