Assume I have a matrix $A$. and $P$ is a permutation matrix.
will the eigenvalue of $A$ be equal to $PA$ or $AP$?
$PA$ and $AP$ means switch $A$'s column or rows.
2026-03-29 18:00:43.1774807243
will eigenvalue of a matrix $A$ change if switch its several rows or columns?
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Yes, the eigenvalues can change. Consider the identity matrix and $\left(\begin{array}{cc} 0 & 1 \\ 1& 0 \end{array}\right)$. (hint: the determinant of the latter matrix has determinant -1)