Variations on a theorem of Ryser (Q1361780)

I have always been disturbed by short proofs of old theorems, because the authors fail to show why these are so important apart from a questionable remark ``while use of algebraic techniques to prove a combinatorial theorem is surely not reprehensible, it is natural to wonder if such techniques are necessary.'' So here is authors' summary regarding symmetric block designs: We present a new, elementary proof of Ryser's theorem and give a characterization of incidence matrices of symmetric block designs that involves eigenvalues.