Matrix solving

Discussion in 'Math' started by switchfoot, Jan 12, 2006.

  1. switchfoot

    Thread Starter New Member

    May 14, 2005
    9
    0
    Hi,

    Can anyone solve this equation for G?

    2(H^T) - (G^T) (H^T) H - G (H^T) H + 2 sigma^2 G =0

    where H and G are square matrices,
    sigma is a scalar and
    T means transpose

    Cheers. :)
     
  2. MEGA_AMPERE

    Member

    Jan 14, 2006
    18
    0
    naaa
    can't read it right
    what is this means ^
     
  3. lex_ph

    New Member

    Jan 15, 2006
    5
    0
    I think that "^" thing represents "raised to". I that case H raised to T and so on.
     
  4. CoulombMagician

    Active Member

    Jan 10, 2006
    37
    0
    T means transpose, flip the matrix around it's diagonal so that the i,j and j,i elements are interchanged.

    A matrix M for which m(i,j) = m(j,i) is said to be symmetric and M^T = M

    if m(i,j) = -m(j,i) it is called antisymmetric and M^T = -M

    Any square matrix G can be written as the sum of a symmetric and an antisymmetric matrix G = Gs + Ga just define Gs = (1/2)*(G + G^T)
    and Ga = (1/2)(G - G^T).

    Obviously ((A^T)^T) = A

    Another property is (AB)^T = (B^T)(A^T) so (A^T)A = A(A^T).
    If A,B are symmetric then (AB)^T = BA

    I'm still trying to crack this nut 5 minutes at a time.
     
  5. The Skeptic

    Well-Known Member

    Dec 27, 2005
    61
    0
    Are you sure nothing else is known about G or H, such s their being symmetrical or something else? Here is the beggining of it. Please forget the last line, I couldn't erase it.
     
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