Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra
From MaRDI portal
Publication:5860469
DOI10.1090/bull/1722zbMath1481.15008arXiv1908.03795OpenAlexW3131825194WikidataQ112628821 ScholiaQ112628821MaRDI QIDQ5860469
Stephen J. Parke, Xining Zhang, Peter B. Denton, Terence C. Tao
Publication date: 19 November 2021
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.03795
Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Research exposition (monographs, survey articles) pertaining to linear algebra (15-02) History of linear algebra (15-03)
Related Items
The Yannelis-Prabhakar theorem on upper semi-continuous selections in paracompact spaces: extensions and applications, Analytical solutions to some generalized and polynomial eigenvalue problems, Equiangular lines in Euclidean spaces: Dimensions 17 and 18, Can one hear a matrix? Recovering a real symmetric matrix from its spectral data, Quantum walks do not like bridges, Eigenvector phase retrieval: recovering eigenvectors from the absolute value of their entries, Quantum dynamics for general time-dependent three coupled oscillators based on an exact decoupling, Imprints of flavor anomalies on neutrino oscillations through dark matter halo, Higher order derivatives of the adjugate matrix and the Jordan form, A divide-and-conquer method for constructing a pseudo-Jacobi matrix from mixed given data, Singular value inequalities of matrix sum in log-majorizations, Proof of a conjecture involving derangements and roots of unity, Eigenvectors from Eigenvalues Sparse Principal Component Analysis, Equiangular lines in low dimensional Euclidean spaces, Eigenvector distribution in the critical regime of BBP transition, Approximate Generalized Inverses with Iterative Refinement for $\epsilon$-Accurate Preconditioning of Singular Systems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Graph reduction techniques and the multiplicity of the Laplacian eigenvalues
- Random matrices: universality of local eigenvalue statistics
- Inverse problems in vibrations.
- On the eigenvalues of principal submatrices of \(J\)-normal matrices
- On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem
- Star complements and exceptional graphs
- Spectral conditions for the reconstructibility of a graph
- Über monotone Matrixfunktionen
- Manifestations of the Schur complement
- Some results on graph spectra
- Semicircle law on short scales and delocalization of eigenvectors for Wigner random matrices
- State transfer in strongly regular graphs with an edge perturbation
- Principal submatrices of normal and Hermitian matrices
- Principal submatrices. II: The upper and lower quadratic inequalities
- Principal submatrices. IV: On the independence of the eigenvalues of different principal submatrices
- When can perfect state transfer occur?
- Fingerprint Databases for Theorems
- Error bounds in the Rayleigh-Ritz approximation of eigenvectors
- Structured inverse eigenvalue problems
- The toda flow on a generic orbit is integrable
- On Cauchy's Inequalities for Hermitian Matrices
- On the eigenvalues of principal submatrices of normal, hermitian and symmetric matrices
- A Stable and Efficient Algorithm for the Rank-One Modification of the Symmetric Eigenproblem
- Limited quantum decay
- Matrix models for beta ensembles
- Some Modified Matrix Eigenvalue Problems
- Finite Dimensional Vector Spaces. (AM-7)
- GUEs and queues
