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.
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.
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.