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# Eigenvalues and operations on matrices

Put content here.**Properties of eigenvalues under matrix operations:**
- If $\lambda$ is an eigenvalue of $A$, then $\lambda^k$ is an eigenvalue of $A^k$
- If $\lambda$ is an eigenvalue of $A$, then $1/\lambda$ is an eigenvalue of $A^{-1}$ (if $A$ invertible)
- If $\lambda$ is an eigenvalue of $A$, then $\lambda + c$ is an eigenvalue of $A + cI$
- If $\lambda$ is an eigenvalue of $A$, then $c\lambda$ is an eigenvalue of $cA$
- Similar matrices have the same eigenvalues

# Parents

* Eigenvalues and eigenvectors