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Everything about Quadratic eigenvalue problem
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues , left eigenvectors and right eigenvectors such that Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Quadratic eigenvalue problemA 5-minute orientation
- Skim a recent paper: New backward error bounds of Rayleigh–Ritz projection methods for quadratic eigenvalue problemInfluential work since 2022
- Pick up a classic book: Linear algebra and its applicationsThe most-reprinted book on the subject
- Read the landmark paper: The Quadratic Eigenvalue ProblemCited 1,119 times
- Go sideways: Nonlinear eigenproblemA closely related topic
- Go sideways: Sylvester equationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The Quadratic Eigenvalue Problem
Regularized Total Least Squares Based on Quadratic Eigenvalue Problem Solvers
The Quadratic Arnoldi Method for the Solution of the Quadratic Eigenvalue Problem
Solutions of the Partially Described Inverse Quadratic Eigenvalue Problem
On the quadratic two-parameter eigenvalue problem and its linearization
Quadratic Residual Bounds for the Hermitian Eigenvalue Problem
Lanczos algorithm for the quadratic eigenvalue problem in engineering applications
Solutions to a quadratic inverse eigenvalue problem
🆕 Influential since 2022
New backward error bounds of Rayleigh–Ritz projection methods for quadratic eigenvalue problem
Solving the quadratic eigenvalue problem expressed in non-monomial bases by the tropical scaling
Singular quadratic eigenvalue problems: linearization and weak condition numbers
Refined isogeometric analysis of quadratic eigenvalue problems
Eigenvalue embedding problem for quadratic regular matrix polynomials with symmetry structures
📚 Books worth reading
Linear algebra and its applicationsDavid C. Lay, Lay · 1994
Mathematical handbook for scientists and engineersGranino Arthur Korn · 1961
Perturbation theory for linear operatorsTosio Katō · 1966
Introduction to Multiple Time Series AnalysisHelmut Lütkepohl, Helmut Lutkepohl · 1991
Numerical linear algebra and applicationsBiswa Nath Datta · 1995
Newtonian Nonlinear Dynamics for Complex Linear and Optimization ProblemsLuis Vázquez · 2012
Linear algebraSeymour Lipschutz · 2012
Coding the MatrixPhilip N. Klein · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Nonlinear eigenproblem In mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the (ordinary) eigenvalue problem to equations…
- Sylvester equation In mathematics, in the field of control theory, a Sylvester equation is a matrix equation of the form: A X + X B = C . {\displaystyle AX+XB=C.} It is named…
- Arrowhead matrix In the mathematical field of linear algebra, an arrowhead matrix is a square matrix containing zeros in all entries except for the first row, first column…
- Sylvester's law of inertia Sylvester's law of inertia is a theorem in matrix algebra about certain properties of the coefficient matrix of a real quadratic form that remain invariant…
- Symmetric matrix In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A is symmetric ⟺ A = A T . {\displaystyle A{\text{…
- Matrix analysis In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular…
- Defective matrix In linear algebra, a defective matrix is a square matrix that does not have a complete basis of eigenvectors, and is therefore not diagonalizable. In particular…
- Numerical range In the mathematical field of linear algebra and convex analysis, the numerical range or field of values or Wertvorrat or Wertevorrat of a complex n × n…