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What is the most basic definition of eigenvalues?


Let A be a square matrix. Its eigenvalues satisfy det(\lambda I-A)=0. But is this the most basic definition of eigenvalues?


The basic definition is: \lambda is an eigenvalue of A if and only if there is a vector v such that

Av=\lambda v

And it is easy to show Av=\lambda v is equivalent to det(\lambda I-A)=0.


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