In linear algebra, an eigenvector of a linear map is a non-zero vector such that applying to results in a vector in the same direction as (including possibly the zero vector). In other words, is an eigenvector for if and only if there is some scalar constant such that . Here, is known as the eigenvalue associated to the eigenvector. The eigenspace of an eigenvalue refers to the set of all eigenvectors that correspond with that eigenvalue, and is a vector space; in particular, it is a subspace of the domain of the map .
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