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eigenvalue
ˈeigenvalue Physics. [tr. G. eigenwert.] One of those special values of a parameter in an equation for which the equation has a solution (see quot. 1938).1927 Nature 23 July 117/1 Among those..trying to acquire a general acquaintance with Schrödinger's wave mechanics there must be many who find thei... Oxford English Dictionary
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Eigenvalue algorithm
to the eigenvalue. If , then and have the same eigenvectors, and is an eigenvalue of if and only if is an eigenvalue of . wikipedia.org
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Eigenvalue Calculator: Wolfram|Alpha
Wolfram|Alpha is a great resource for finding the eigenvalues of matrices. You can also explore eigenvectors, characteristic polynomials, invertible matrices, diagonalization and many other matrix-related topics. Learn more about: Eigenvalues; Tips for entering queries. Use plain English or common mathematical syntax to enter your queries.
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Eigenvalue perturbation
problem Setting of perturbation for a generalized eigenvalue problem Suppose we have solutions to the generalized eigenvalue problem, where and are Eigenvalue perturbation: a theoretical basis. wikipedia.org
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"$1$ is an eigenvalue of $A^n$" implies an eigenvalue of $A$ is a root of unity? Let $A$ be a square matrix. If $1$ is an eigenvalue of $A^n$, then is it true that there is an eigenvalue of $A$ which is a root of unity?
Let the eigenvalues of $A$ are $\lambda_1, \dots, \lambda_k$. That implise, that $A^n$ has the eigenvalues $\lambda_1^n, \dots, \lambda_k^n$. If some of $\lambda_i^n =1$, that implies $\lambda_i$ is the $n$-th root of unity.
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Normal eigenvalue
Definition of a normal eigenvalue An eigenvalue of a closed linear operator in the Banach space with domain is called normal (in the original terminology If is a normal eigenvalue, then the root lineal coincides with the range of the Riesz projector, . wikipedia.org
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if $\lambda$ is an eigenvalue of A and an eigenvalue of B is it also an eigenvalue of AB? The question is essentially explained in the title: given that $\lambda$ is an eigenvalue of an $n \times n$ matrix A and anoth...
No; consider the matrices $A=B=\begin{pmatrix}2&0\\\0&2\end{pmatrix}$, or more generally $A=B=\lambda I$ with $\lambda\neq0,1$.
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Dirichlet eigenvalue
The Dirichlet eigenvalues are found by solving the following problem for an unknown function u ≠ 0 and eigenvalue λ Here Δ is the Laplacian, which is Thus they can be arranged in increasing order: where each eigenvalue is counted according to its geometric multiplicity. wikipedia.org
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Jacobi eigenvalue algorithm
The Jacobi eigenvalue method repeatedly performs rotations until the matrix becomes almost diagonal. The logical array changed holds the status of each eigenvalue. wikipedia.org
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Divide-and-conquer eigenvalue algorithm
Divide-and-conquer eigenvalue algorithms are a class of eigenvalue algorithms for Hermitian or real symmetric matrices that have recently (circa 1990s) In certain cases, it is possible to deflate an eigenvalue problem into smaller problems. wikipedia.org
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特征值（eigenvalue）特征向量（eigenvector）特征值分解（eigenvalue decomposition）
特征值与特征向量我们知道，矩阵乘法对应了一个变换，是把任意一个向量变成另一个方向或长度都大多不同的新向量。在这个变换的过程中，原向量主要发生旋转、伸缩的变化。如果矩阵对某一个向量或某些向量只发生伸缩…
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Perturbative solution to the Lane-Emden equation: an eigenvalue ...
Abstract. Under suitable scaling, the structure of self-gravitating polytropes is described by the standard Lane-Emden equation (LEE), which is characterized by the polytropic index n.Here, we use the known exact solutions of the LEE at n = 0 and n = 1 to solve the equation perturbatively.We first introduce a scaled LEE (SLEE) where polytropes with different polytropic indices all share a ...
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Compressed Cooperative Eigenvalue Spectrum Sensing for Radio Signal
Compressed Cooperative Eigenvalue Spectrum Sensing for Radio Signal . Abstract . Abstract: Detecting the abnormal radio emission through radio monitoring is an important task of radio
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[Eigenvalue analysis of wideband acoustic immittance in secretory ...
Mar 1, 2022Europe PMC is an archive of life sciences journal literature.
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Quadratic eigenvalue problem
In mathematics, the quadratic eigenvalue problem (QEP), is to find scalar eigenvalues , left eigenvectors and right eigenvectors such that where , with One approach is to transform the quadratic matrix polynomial to a linear matrix pencil (), and solve a generalized eigenvalue problem. wikipedia.org
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