- In
linear algebra, an
eigenvector (/ˈaɪɡən-/ EYE-gən-) or
characteristic vector is a
vector that has its
direction unchanged (or reversed) by a given...
- In
linear algebra, a
generalized eigenvector of an n × n {\displaystyle n\times n}
matrix A {\displaystyle A} is a
vector which satisfies certain criteria...
- In
graph theory,
eigenvector centrality (also
called eigencentrality or
prestige score) is a
measure of the
influence of a node in a
connected network...
- of
largest magnitude and that
eigenvalue is real. The
corresponding eigenvector can be
chosen to have
strictly positive components, and also ****erts...
-
concerned with
walks of
length one (degree centrality) to
infinite walks (
eigenvector centrality).
Other centrality measures, such as
betweenness centrality...
- jth
eigenvector.
Matrix V
denotes the
matrix of
right eigenvectors (as
opposed to left
eigenvectors). In general, the
matrix of
right eigenvectors need...
- form,
whereby the
matrix is
represented in
terms of its
eigenvalues and
eigenvectors. Only
diagonalizable matrices can be
factorized in this way. When the...
- and a
nonzero vector v {\displaystyle v} ,
which is a
corresponding eigenvector of λ {\displaystyle \lambda } , that is, A v = λ v {\displaystyle Av=\lambda...
- also find
eigenvectors.
Given an n × n
square matrix A of real or
complex numbers, an
eigenvalue λ and its ****ociated
generalized eigenvector v are a pair...
-
there exists an
ordered basis of V {\displaystyle V} consisting of
eigenvectors of T {\displaystyle T} .
These definitions are equivalent: if T {\displaystyle...
