@Carl Love Ok I see.  Thanks for clearing that up.  It's strange which statements Maple can and can't verify.

@acer Again this code yields a FAIL result.  

restart; 
with(LinearAlgebra):
assume(y11, real); 
assume(y12, real); 
assume(y21, real); 
assume(y22, real); 
assume(y31, real); 
assume(y32, real); 
Y := Matrix([[y11, y12], [y21, y22], [y31, y32]]):
assume(w11, RealRange(0, 1)); 
assume(w12, RealRange(0, 1));
assume(w13, RealRange(0, 1)); 
assume(w22, RealRange(0, 1));
assume(w23, RealRange(0, 1));
assume(w33, RealRange(0, 1)); 
W := Matrix([[w11, w12, w13], [w12, w22, w23], [w13, w23, w33]]):
d := Matrix(W . Matrix(3, 3, 1), shape = diagonal):
R := simplify(Trace(simplify(Transpose(Y).(d - W).Y))):
is(R >= 0)