Eigenvalue
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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