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Eigenvector

Overview [1] [2]#

Eigenvector or characteristic vector of a linear transformation is a non-zero vector that only changes by an overall scale when that linear transformation is applied to it.

More formally, if T is a linear transformation from a vector space V over a field F into itself and v is a vector in V that is not the zero vector, then v is an Eigenvector of T if T(v) is a scalar multiple of v. This condition can be written as the equation

T(V) =λv

Below Matrix A acts by stretching the vector x, not changing its direction, so x is an Eigenvector of A.

https://upload.wikimedia.org/wikipedia/commons/thumb/5/58/Eigenvalue_equation.svg/500px-Eigenvalue_equation.svg.png

More Information#

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