Do all square matrices have eigenvectors?

I came across a video lecture in which the professor stated that there may or may not be any eigenvectors for a given linear transformation.

But I had previously thought every square matrix has eigenvectors.


It depends over what field we’re working. For example, the real matrix


has no eigenvalues at all (i.e., over R ), yet the very same matrix defined over the complex field C has two eigenvalues: ±i

Source : Link , Question Author : Saurabh U. Shringarpure , Answer Author : DonAntonio

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