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A question on matrices properties

  1. Jan 5, 2008 #1
    there is some property of matrices that i forgot
    that says that for some kind of matrices there is a given number

    that if we will put the given martices to the power of this given number
    it will get the zero matrices

    for example
    0 a
    a b

    in the power of 3 will change for the first time to
    0 0
    0 0

    what are the laws for this number 3

    how do i know the number by looking at the given matrices
     
  2. jcsd
  3. Jan 5, 2008 #2

    morphism

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    Such a matrix A is called "nilpotent", and the smallest natural number n such that An=0 is usually called the "index of nilpotence". Try googling for information -- you'll find a lot.
     
  4. Jan 5, 2008 #3
    i read about them
    i understood the transformation
    of each step

    but i was told the the number comes from the size of the given matrices
    which is not true in the case that i showed

    the only way that i can find out the number is by practicly
    step by step multiplying the matrix by itself.

    is there an yeasier way??
     
  5. Jan 5, 2008 #4

    morphism

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    I'm not familiar with any easier general method.
     
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