This is true for many examples I can think of, but can we always say that?
2026-04-07 22:59:22.1775602762
Is the sum of geometric multiplicities of non zero eigenvalues also the rank of a matrix?
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No, this is not true in general. For instance, the matrix $$\begin{bmatrix}1&1\\0&1\end{bmatrix}$$ has rank $2$, but the sum of the geometric multiplicities of the non-zero eigenvalues is $1$.