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Matrix Operations

  1. Feb 4, 2009 #1
    If I have a matrix

    S =

    0 0 0 0 ... 0
    1 0 0 0 ... 0
    0 1 0 0 ... 0
    0 0 1 0 ... 0
    ...
    0 0 0 0 .1.0


    S^2 =


    0 0 0 0 ... 0
    0 0 0 0 ... 0
    1 0 0 0 ... 0
    0 1 0 0 ... 0
    ...
    0 0 0 0 1.. 0


    etc.

    going in this way S^n would just be the zero matrix.,
    How do I generalize S^n of this matrix?
     
  2. jcsd
  3. Feb 4, 2009 #2

    lurflurf

    User Avatar
    Homework Helper

    If S is a lower triangular matrix (n by n), S^n is the zero matrix.
    Now prove.
     
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