- for the Perron–Frobenius is one-dimensional. ****uming
there exists an
eigenpair (λ, y) for A, such that
vector y is positive, and
given (r, x), where...
- the
vector is
called simply an eigenvector, and the pair is
called an
eigenpair. In this case, Av = λv. Any
eigenvalue λ of A has
ordinary eigenvectors...
-
iteration is a super-linear and
deterministic method to
compute the
largest eigenpair.
Rayleigh quotient iteration Inverse iteration Richard von
Mises and H...
- (nonlinear) eigenvector, and ( λ , x ) {\displaystyle (\lambda ,x)} as the
eigenpair. The
matrix M ( λ ) {\displaystyle M(\lambda )} is
singular at an eigenvalue...
-
competitive with
those of the
Lanczos method,
computing a
single extreme eigenpair of a
symmetric matrix.
Linear convergence is
theoretically guaranteed...
- ) {\displaystyle (\lambda _{i},v_{i})} is the i {\displaystyle i} -th
eigenpair after orthonormalization and y i = v i ∗ x {\displaystyle y_{i}=v_{i}^{*}x}...
- is simple,
since if wi is zero, ( e i {\displaystyle e_{i}} ,di) is an
eigenpair ( e i {\displaystyle e_{i}} is in the
standard basis) of D + w w T {\displaystyle...
-
spectral theorem applies to C {\displaystyle {\mathcal {C}}} ,
yielding eigenpairs ( λ j , φ j ) {\displaystyle (\lambda _{j},\varphi _{j})} , so that in...
- {\displaystyle (\alpha e^{-i\theta },{\widehat {U}}|\alpha \rangle )} is the
eigenpair of a ^ U ^ | α ⟩ {\displaystyle {\widehat {a}}{\widehat {U}}|\alpha \rangle...
- λ i ) i = 1 n {\displaystyle (v_{i},\lambda _{i})_{i=1}^{n}} be the
eigenpairs of A. Due to the
symmetry of A, all v i {\displaystyle v_{i}} and λ i...
