Results 1 to 2 of 2

Thread: Determine nullity when matrix power =0

  1. #1
    Newbie
    Joined
    Aug 2011
    Posts
    2

    Determine nullity when matrix power =0

    If M^(n-1) notequal 0 but $\displaystyle , 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


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Determine nullity when matrix power =0

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

Similar Math Help Forum Discussions

  1. Matrix rank and nullity
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: Mar 16th 2011, 01:21 AM
  2. Determine the content of a matrix
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: Nov 14th 2010, 05:57 AM
  3. Please help to determine the power of a hypothesis test
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: Apr 30th 2010, 10:08 PM
  4. Nullity of a a 3x3 matrix
    Posted in the Advanced Algebra Forum
    Replies: 15
    Last Post: Jan 1st 2010, 07:01 AM
  5. power series, determine radius of convergence.
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Apr 22nd 2007, 10:27 PM

Search Tags


/mathhelpforum @mathhelpforum