# Non-derogatory matrix

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An square matrix $A$ for which the characteristic polynomial and minimal polynomial coincide (up to a factor $\pm1$). Equivalently, for each of its distinct eigenvalues $\lambda$ there is, in the Jordan normal form for $A$, only one Jordan block with that eigenvalue $\lambda$; this is in turn equivalent to each distinct eigenvalue having only one independent eigenvector, that is, geometric multiplicity one.