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.
Answer
It depends over what field we’re working. For example, the real matrix
A=(0−110)
has no eigenvalues at all (i.e., over R ), yet the very same matrix defined over the complex field C has two eigenvalues: ±i
Attribution
Source : Link , Question Author : Saurabh U. Shringarpure , Answer Author : DonAntonio
