How to intuitively understand eigenvalue and eigenvector?

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Intuition behind eigenvalues and eigenvectors.

  • Eigenpairs are a lot like the roots of a polynomial. While roots of a polynomial ground the polynomial(fix its shape), eigenvalues limit the behavior of the linear transformation.

  • The eigenvalues of a linear mapping is a measure of the distortion induced by the transformation and the eigenvectors tell you about how the distortion is oriented.

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Bhavishya
CS undergrad @IITK