An eigenvector of an operator is a vector such that the action of the operator is the same as multiplication by a constant, called the eigenvalue. The eigensystem of an operator is the set of all such eigenvectors and their associated eigenvalues.
Questions tagged [eigensystem]
184 questions
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Using algebraically smallest eigenvalues to find smallest in magnitude eigenvalues
I have a symmetric indefinite matrix, $H$. I also have a routine that can compute the algebraically smallest eigenvalues of a symmetric indefinite matrix. I would like to compute the eigenvalues with smallest magnitude using my existing code.
One…
dranxo
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Time-stable spectral decomposition algorithm
Consider an $n \times n$ real, time-dependent matrix $A(t)$ such that $A(t) = A(t)^{T} > 0$ and $A(t)$ is continuous on $[a,b]$. Then it is posible to specify a matrix $S(t) \in SO(n)$ such that $S(t)A(t)S^{T}(t) = \Lambda(t)$, where $\Lambda$ is a…
Appliqué
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On implementations of the complex QR decomposition
I have an mathematical theorem on the QR decomposition, which relies on the QR decomposition of an invertible square complex matrix always constructing a triangular matrix with real diagonal entries.
While at least in Octave this seems to be true, I…
shuhalo
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Finding dominant eigenvectors of an operator that is small but costly to evaluate
Suppose I have a symmetric linear operator $A:\mathbb{R}^k \rightarrow \mathbb{R}^k$ where $k$ is "small" (eg., $k=100$), and I want to find it's first few eigenvectors, (eg., $10$ eigenvectors).
If we had a matrix representation of $A$ this would…
Nick Alger
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last column of SPD matrix given it's spectral decomposition
I'm working on this application where
I get the spectral decomposition (O,D) of a matrix A for free (A is of full rank) but not A itself, and I need to only recover the last column of A. I was wondering if there was a more efficient way to do this…
user189035
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how can I numerically calculate all eigenvectors of a $n \times n$ complex tridiagonal matrix?
I have tried matlab eig command, it results true eigenvalues but wrong eigenvectors.
I also tried direct iteration with rayleigh qotient which is better but doesn't give all eigenvectors
also I have tried QR method which gives eigenvalues but not…
lili
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When numerically computing eigenstates during a coupled-mode-space NEGF calculation, do phases matter?
The coupled mode space NEGF method for computing transistor characteristics involves expanding the electronic wavefunction in a mode space basis
$$\Psi(x,y,z) = \sum_n\phi_n(x)\xi_n(y,z;x)$$
where $\xi_n(y,z;x)$ is the nth mode at position x (the x…
DJames
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Coupled system of differential equations with eigenvalue
I have the following system of coupled differential equations (the Bogoliubov-de Gennes equations for a certain geometry):
$$
\begin{cases}
-\frac{1}{2}u''(r) + \big[\frac{1}{2r^2} + f_1(r)\big]u(r) + f_2(r)v(r)=\omega u(r)\\
-\frac{1}{2}v''(r) +…
Funzies
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Efficient Eigen Solver
I am working on a flow physics problem (2D), which ultimately boils down to solving Eigen value problem. Even for a grid size of 60 x 60, the matrix in the Eigen value problem end up with 1260 million elements (This matrix has to be solved…
Rhinocerotidae
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