Results 1 to 3 of 3

Math Help - Diagonalizable problem

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Diagonalizable problem

    Suppose that A is nxn matrix with two distinct eigenivalues a and b, and the eigenspace of a is n-1, prove that A is diagonalizable
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,672
    Thanks
    302
    Awards
    1
    Quote Originally Posted by tttcomrader View Post
    Suppose that A is nxn matrix with two distinct eigenivalues a and b, and the eigenspace of a is n-1, prove that A is diagonalizable
    I'm confused. Taking a (admittedly quick) look at the problem it would appear to me that this is merely a question about if we have a degenerate eigenvalue can we diagonalize the matrix?

    If we have a matrix with two eigenvalues (each with degenerate eigenspaces to be general) we can always put the matrix in block diagonal form. So the question should become whether we can diagonalize an n x n matrix that has an n degenerate eigenvalue.

    Please let me know if I'm over-simplifying things and missed something.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2
    Basically, A has two distinct eigenvalue, one of them has n-1 possible eigenvector corespond to it.

    I'm stuck on trying to show that the multiplicity of eigenvalue a is n-1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Don't understand this diagonalizable matrix problem?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 2nd 2012, 12:28 AM
  2. diagonalizable
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 15th 2011, 07:53 AM
  3. diagonalizable
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 25th 2010, 02:32 AM
  4. Diagonalizable
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: May 4th 2010, 07:48 PM
  5. diagonalizable
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: July 23rd 2008, 11:10 AM

Search Tags


/mathhelpforum @mathhelpforum