= Solution
Factor the coefficients into a <tensor product>:
$$
|\Psi\rangle
=\left(\frac{|0\rangle-|1\rangle}{\sqrt2}\right)_A
\otimes\left(\frac{|0\rangle-|1\rangle}{\sqrt2}\right)_B.
$$
This is already a <Schmidt decomposition> with one term. Consequently
$$
\boxed{r=1,\qquad s_1=1,\qquad\lambda_1=1.}
$$
Each <reduced density matrix> is the rank-one <orthogonal projector> onto $(|0\rangle-|1\rangle)/\sqrt2$, so its other <eigenvalue> is zero. The joint <pure state> is a <product state>, with no <entanglement>.
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