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