An eigenvector is defined as a non-zero vector 'v' such that A.v = λ.v(adsbygoogle = window.adsbygoogle || []).push({});

I don't understand the motive behind this. We are trying to find a vector that when multiplied by a given square matrix preserves the direction of the vector.

Shouldn't the motive be the opposite i.e. finding the matrix A given the vector v?

I suppose eigenvector was defined this way with some application in mind

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# Motivation behind eigenvalue and eigenvector

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