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Plus, our experts are waiting 24/ 7 to answer virtually all of. In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non- zero vector that changes by only a scalar factor 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.