Matrix solving

[switchfoot]

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. :)

[MEGA_AMPERE]

naaa
can't read it right
what is this means ^

[lex_ph]

I think that "^" thing represents "raised to". I that case H raised to T and so on.

[CoulombMagician]

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.

[The Skeptic]

Originally posted by switchfoot@Jan 13 2006, 02:54 AM
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. :)
Quoted post


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.