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Linearly independent, matrix

  1. Feb 11, 2014 #1
    Why column 1 is M^2*v? How can we know?

    Please see attached. Many thanks.
     

    Attached Files:

  2. jcsd
  3. Feb 11, 2014 #2

    tiny-tim

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    hi victoranderson! :smile:

    if Q-1MQ = that matrix,

    then MQ = Q(that matrix), which is … ? :wink:
     
  4. Feb 11, 2014 #3
    I know what you mean
    Let that matrix be D
    I can find MQ=QD by trail and error
    Is there any other method I can use to find the columns of Q without trial and error?
     
  5. Feb 12, 2014 #4

    tiny-tim

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    hi victoranderson! :smile:

    (just got up :zzz:)
    it isn't trial and error

    what are the columns of QD ? :wink:
     
  6. Feb 22, 2014 #5
    it's been a long time..

    The columns of QD is [0,0,0]^T, [1,1,-1]^T and [2,3,1]^T
    which are ##M^3v , M^2v , Mv ## respectively

    I am stupid and I still do not understand..
     
    Last edited: Feb 22, 2014
  7. Feb 22, 2014 #6

    tiny-tim

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    hi victoranderson! :smile:

    for any matrix P with columns A B C:

    the columns of PD are 0 A B

    the columns of MP are MA MB MC​

    so MP = PD (ie P-1MP = D) if 0 = MA, A = MB, B = MC

    (so A = MB = M2C and M3C = 0)

    so we choose the columns of P to be M2 MC and C :smile:

    (and then we call it Q instead of P)
     
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