After viewing the 3blue1brown video on Duality, I am just seeing xT*A*x as the results of applying a linear transformation to a vector x and then projecting that new vector back onto x; if the vectors still point "in the same direction" i.e. the projection is positive, then A is positive definite####[['3blue1brown video on Duality', 'Course_General_Feedback', 'NEU']]