Live briefing
Everything about Generalized eigenvector
Vector satisfying some of the criteria of an eigenvector
In linear algebra, a generalized eigenvector of an matrix is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Generalized eigenvectorA 5-minute orientation
- Skim a recent paper: A generalized eigenvector centrality for multilayer networks with inter-layer constraints on adjacent node importanceInfluential work since 2022
- Pick up a classic book: Modal ring method for the scattering of soundThe most-reprinted book on the subject
- Read the landmark paper: Soft self-consistent pseudopotentials in a generalized eigenvalue formalismCited 22,324 times
- Go sideways: Eigenvalues and eigenvectorsA closely related topic
- Go sideways: Jordan normal formA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Soft self-consistent pseudopotentials in a generalized eigenvalue formalism
Eigenvalue-generalized eigenvector assignment with state feedback
Eigenvalue-generalized eigenvector assignment by output feedback
Generalized eigenvector algorithm for blind equalization
Fast Generalized Eigenvector Tracking Based on the Power Method
A Unified Assessment of Fast Floquet, Generalized Floquet, and Periodic Eigenvector Methods for Rotorcraft Stability Predictions
Riesz basis property of the generalized eigenvector system of a Timoshenko beam
Eigenvector Derivatives of Generalized Nondefective Eigenproblems With Repeated Eigenvalues
🆕 Influential since 2022
A generalized eigenvector centrality for multilayer networks with inter-layer constraints on adjacent node importance
Multiscale Continuous and Discrete Spatial Heterogeneity Analysis: The Development of a Local Model Combining Eigenvector Spatial Filters and Generalized Lasso Penalties
Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh–Ritz procedure for generalized Hermitian eigenvalue problems
Adaptive Generalized Eigenvector Estimating Algorithm for Hermitian Matrix Pencil
Convergence of local eigenvector processes of generalized Wigner matrices
📚 Books worth reading
- 📕Modal ring method for the scattering of soundKenneth J. Baumeister · 1993
- 📕A panorama of mathematicsCarlos M. da Fonseca · 2016
- 📕Linear Algebra IFrederick P. Greenleaf, Sophie Marques · 2019
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Eigenvalues and eigenvectors In linear algebra, an eigenvector (/ˈaɪɡən-/ EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by…
- Jordan normal form [⌜λ11⌝λ11⌞λ1⌟⌜λ21⌝⌞λ2⌟[λ3]⋱⌜λn1⌝⌞λn⌟] Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known…
- Eigendecomposition of a matrix In linear algebra, eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A into a canonical form given by A=QDQ−𝟣…
- Characteristic polynomial In linear algebra, the characteristic polynomial of a square matrix is a polynomial which is invariant under matrix similarity and has the eigenvalues…
- Companion matrix In linear algebra, the Frobenius companion matrix of the monic polynomial p(x)=c0+c1x+⋯+cn−1xn−1+xn is the square matrix defined as C(p)=[00…0−c010…0−…
- Eigenvalue algorithm In numerical analysis, one of the most important problems is designing efficient and stable algorithms for finding the eigenvalues of a matrix. These eigenvalue…
- Modal matrix In linear algebra, the modal matrix is used in the diagonalization process involving eigenvalues and eigenvectors. Specifically the modal matrix M {\displaystyl…
- Spectrum of a matrix In mathematics, the spectrum of a matrix is the set of its eigenvalues. (More precisely, it is its multiset of eigenvalues, where each eigenvalue comes…