= Linear latent coordinates are not unique without constraints
In the observation model $y=Cz+b$, let $Q$ be an <orthogonal matrix>. Replacing $z$ by $Qz$ and $C$ by $CQ^T$ leaves $y$ unchanged because $Q^TQ=I$. Thus reconstruction alone does not give each latent axis a unique biological meaning. A particular stochastic model can restrict this symmetry through its prior and parameter constraints; the algebra does not claim every fitted latent model has every rotational ambiguity.
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