  A priori, a posteriori, and mixed type upper bounds for the absolute change
in Ritz values of self-adjoint matrices in terms of submajorization relations
are obtained. Some of our results prove recent conjectures by Knyazev,
Argentati, and Zhu, which extend several known results for one dimensional
subspaces to arbitrary subspaces. In addition, we improve Nakatsukasa's version
of the $\tan \Theta$ theorem of Davis and Kahan. As a consequence, we obtain
new quadratic a posteriori bounds for the absolute change in Ritz values.
