Results 1 to 4 of 4

Math Help - Eigenvalues/orthogonality/diagonalization

  1. #1
    Junior Member krtica's Avatar
    Joined
    Apr 2010
    Posts
    26

    Eigenvalues/orthogonality/diagonalization

    Are all the following statements true?

    Any subspace of R^n has an orthogonal basis.
    Every square matrix is diagonalizable.
    0 vector is an eigenvector of every square matrix.
    If B=P^(-1)AP then A and B have the same eigenvalues.
    Every linear transformation has an eigenvalue.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by krtica View Post
    Are all the following statements true?

    Any subspace of R^n has an orthogonal basis.
    Every square matrix is diagonalizable.
    0 vector is an eigenvector of every square matrix.
    If B=P^(-1)AP then A and B have the same eigenvalues.
    Every linear transformation has an eigenvalue.

    Yes, no, yes, yes, it depends (in the definition field? Not necessarily; in some field extension? Yes, always)

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member krtica's Avatar
    Joined
    Apr 2010
    Posts
    26
    Thank you! Can you please explain why the second statement is false?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Mar 2010
    From
    Florida
    Posts
    3,093
    Thanks
    5
    In this thread you will find 2 or 3 matrices that aren't diagonalizable.

    http://www.mathhelpforum.com/math-he...ponential.html
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Eigenvalues and Diagonalization
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: November 30th 2011, 04:42 AM
  2. orthogonality
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 25th 2009, 10:58 PM
  3. Eigenvalues, Eigenvectors and Diagonalization
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 17th 2009, 08:36 AM
  4. Eigenvectors/Eigenvalues & Diagonalization
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: November 17th 2008, 12:18 AM
  5. Orthogonality
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: May 14th 2008, 11:20 PM

Search Tags


/mathhelpforum @mathhelpforum