The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.

Created almost 9 years ago, updated about 8 hours ago

If $Av=\lambda v$ with $v\ne0$, then $(cA)v=(c\lambda)v$. For $c\ne0$, all eigenvalues of $cA$ arise this way. For $c=0$ in positive dimension, $cA$ is zero and every nonzero vector is a zero-eigenvalue eigenvector.

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