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Math Help - Determine nullity when matrix power =0

  1. #1
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    Determine nullity when matrix power =0

    If M^(n-1) notequal 0 but , M^n=0 , then determine dim ker (M)

    I feel the following two equations and rank nullity theorem can be used for this but not sure how


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  2. #2
    Super Member girdav's Avatar
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    Re: Determine nullity when matrix power =0

    Let x such that M^{n-1}x\neq 0. Show that the vectors x,Mx,\ldots,M^{n-1}x are linearly independent. Therefore, the family \mathcal B=\{M^jx\}_{0\leq j\leq n-1} is a basis of the vector space in which we are working. Write the endomorphism associated to M in the basis \mathcal B.
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