The following code yields "false" for the trace being non-negative.  This, however, is incorrect.

A look at the final expression for the trace shows it is a sum of products of positive values.

Does anyone know what the problem is?

restart;

with(LinearAlgebra);

n := 3;

p := 2;

Y := Matrix(n, p, symbol = y);

W := Matrix(n, n, symbol = w, shape = symmetric);

for i from 1 to n do

for j from 1 to n do

assume(w[i, j], RealRange(0, 1))

end do:

end do:

d := DiagonalMatrix(W . Matrix(n, 1, 1))

is(simplify(Trace(simplify(Transpose(Y) . (d-W) . Y))) >= 0)