Results 1 to 2 of 2

Math Help - realtion between trace of product of two matrices and their eigenvalues

  1. #1
    Junior Member
    Joined
    Jun 2013
    From
    United States
    Posts
    28
    Thanks
    5

    realtion between trace of product of two matrices and their eigenvalues

    A is a symmetric matrix containing only 0s and 1s; in particular all the diagonal entries are 0. B is a symmetric positive definite matrix. I am interested in T = \mathrm{trace}(AB). Is there a simple relation between T and the eigenvalues of A and B?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member ILikeSerena's Avatar
    Joined
    Dec 2011
    Posts
    733
    Thanks
    121

    Re: realtion between trace of product of two matrices and their eigenvalues

    Nope.

    Counter example:

    A=\begin{pmatrix}0&1\\1&0\end{pmatrix}

    B=\begin{pmatrix}1&0\\0&2\end{pmatrix} respectively B=\begin{pmatrix}-1/2&3/2\\3/2&-1/2\end{pmatrix}

    Both versions of B have the same positive eigenvalues, but the trace of AB is different.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. problem on Trace of the sum of two matrices
    Posted in the Advanced Algebra Forum
    Replies: 7
    Last Post: October 17th 2012, 10:36 AM
  2. Proof of trace of product of vector and matrices
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: June 15th 2012, 12:17 AM
  3. Basis for matrices of trace 0
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 30th 2010, 06:29 AM
  4. Trace of a tensor product
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: March 26th 2010, 03:15 AM
  5. Matrices- Trace
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 22nd 2009, 03:06 PM

Search Tags


/mathhelpforum @mathhelpforum