Results 1 to 3 of 3

Math Help - totaly positive matrix method

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    totaly positive matrix method

    cant understand the way the book tests if a matrix is totaly positive(dont know the proper term)
    we need to show that \sum_{i=1}^{2}\sum_{j=1}^{2}a_{ij}k_{i}\overline{k  _{j}}>0
    ihave this matrix but
    \left(\begin{array}{cc}0 & i\\-i & 0\end{array}\right)
    so they choose k_{1}=1 k_{2}=0 and got that the expession is =0
    but we have 4 members here
    so we need k for each member thus we need 4 k's
    why 2?
    cant understand how this method works
    ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,996
    Thanks
    1130

    Re: totaly positive matrix method

    The phrase you want is "positive definite". However, the definition of "positive definite" varys depending on the type of matrix (real entries, complex entries, complex entries and the matrix is Hermitian). What kind of matrices are you dealing with and what is your definition of "positive definite"? (What you want to prove looks awfully like one of the definitions.)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    Re: totaly positive matrix method

    yes if its hermitic and this double sum its bigger and zero
    then its positive definite.

    its matrices in complex field

    but i dont understand how this double sum condition works

    i am stuck on this 2x2 matrices given above

    ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Totaly easy limit :)
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 27th 2010, 02:17 PM
  2. positive matrix
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: October 16th 2010, 01:10 AM
  3. Positive semidefinite matrix
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: February 15th 2010, 01:54 PM
  4. 2x2 Positive Definite matrix.
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: September 10th 2009, 04:39 PM
  5. positive definite matrix
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 26th 2008, 09:57 AM

Search Tags


/mathhelpforum @mathhelpforum