Our Lord and Savior Jeffrey Chasnov. There's no way I'd be able to understand all of this by myself. You truly are a blessing to all of us self-taught students out here
It took me some time to figure it out, but the idea is that we simply take a projection of X_p+1 onto X_p, so X_p transposed is just a part of the projection formula. The idea of the projection is such that you find some coefficient, which when multiplied by X_p, would produce such a scaled version of X_p that is the closest to X_p+1. We know that when p is sufficiently large, both X_p+1 and X_p are simply some multiples of e1, so they are collinear, which means X_p+1 can be expressed as X_p multiplied by some coefficient and that is the coefficient that projection gives us. Now if we look at the formulas of X_p+1 and X_p, the difference between them is just an extra multiple of lambda, so lambda = projection coefficient of X_p+1 onto X_p.
did you learned how to write backwards just so that you could lecture from behind a glass pane strictly to not be in the way of the camera/student view? If so i commend educators like yourself, thank you