  In a 1918 paper Schur proved a remarkable inequality that related group
representations, Hermitian forms and determinants. He also gave concise
necessary and sufficient conditions for equality. In 1964, Marcus gave a
beautiful short proof of Schur's inequality by applying the Cauchy-Schwarz
inequality to symmetric tensors, but he did not discuss the case of equality.
In 1969, Williamson gave an inductive proof of Schur's equality conditions by
contracting Marcus's symmetric tensors onto lower dimensional subspaces where
they remained symmetric tensors. Here we unify these results notationally and
conceptually, replacing contraction operators with the more geometrically
intuitive projection operators.
