I am reading a derivation of conditional multivariate distribution, I have checked many time the following equation, I think it is wrong. $u$ and $v$ are any vectors, and $A$ is symmetric matrix.
The source is from a online webpage: http://fourier.eng.hmc.edu/e161/lectures/gaussianprocess/node7.html $ \begin{eqnarray} &&u^TAu-2u^TAv+v^TAv=u^T Au-u^TAv-u^TAv+v^TAv \nonumber \\ &=&u^TA(u-v)-(u-v)^TAv=u^TA(u-v)-v^TA(u-v) \nonumber \\ &=&(u-v)^TA(u-v)=(v-u)^TA(v-u) \nonumber \end{eqnarray} $
Would any one confirm me this is wrong?