# Is eigenvalue multiplied by constant also an eigenvalue?

Mathematics Asked by Ruby Cho on January 7, 2022

Let $$A$$ be an $$n × n$$ matrix.

If $$lambda$$ is an eigenvalue of $$A$$ and $$c$$ is a nonzero scalar, then $$clambda$$ is another eigenvalue of $$A$$.

I found this on "Linear Algebra and its applications (Jim Defranza)", summary of Chapter 5.

It is acceptable, that eigenvectors multiplied by constant is ok, cause $$A(cv) = cAv = clambda v = lambda(cv)$$.

But I don’t understand $$clambda$$ is also an eigenvalue of $$A$$.

Thank you.

Great question, and good catch!

It's a typo/brain-o. The author surely meant to write "If $$v$$ is an eigenvector of $$A$$ and ..."

Answered by John Hughes on January 7, 2022

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