We give a simple proof that an n x n orthogonal matrix with n greater than or equal to 2 which cannot be written as a direct sum has at least 4n - 4 nonzero entries.
Rocky Mountain Journal of Mathematics
Shader, Bryan L. (1997). "A Simple Proof of Fiedler's Conjecture Concerning Orthogonal Matrices." Rocky Mountain Journal of Mathematics 27.4, 1239-1243.