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Eigenvalues and operations on matrices

Created over 8 years ago, updated 10 days ago

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