= Gauge transformation of a linear differential system
{title2=$A G=G'+G\Lambda$}
Writing $Y=GZ$ with an invertible <matrix>-valued function gives $Z'=\Lambda Z$ exactly when $\Lambda=G^{-1}AG-G^{-1}G'$. For a <formal power series> transformation at an <irregular singular point>, coefficient comparison recursively removes off-diagonal terms when leading diagonal <eigenvalues> are distinct. This is a differential-system change of frame, not specifically an electromagnetic gauge transformation.
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