I asked this question here, however the title of the thread (and the thread itself) was sloppy and unclear.I could not find a way to delete or edit. This is for a regression analysis course, and I've only taken one introductory course on linear algebra, so when I Google'd "finding a symmetric matrix" a lot of stuff that I didn't understand came up. 1. The problem statement, all variables and given/known data Find the unique symmetric matrix A such that Y'AY=Y'GY 2. Relevant equations 3. The attempt at a solution Y'AY = Y'GY Y'AYY'=Y'GYY' Y'AYY'(YY')^-1 = Y'GYY'(YY')^-1 Y'A=Y'G YY'A=YY'G (YY')^-1YY'A=YY')^-1YY'G A=G However, G is not symmetric: G= [1.0 1 1.0 -1.0 0 1.0 0.5 2 -0.5] Other than the algebraic manipulation above, I don't know how else to approach this problem.