Questions tagged [symmetry]
For questions about exploiting symmetries to solve computational problems. This could include seeking an algorithm for symmetric matrices or finding machine learning descriptors that are invariant under certain symmetry operations.
8 questions with no upvoted or accepted answers
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Are there any standardized file formats for point group character tables?
Character tables are an important tool for symmetry analysis in many computational chemistry software packages. Are there any standardized file formats for point group character tables?
This may seem ...
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How can Navier--Stokes equations have asymmetric solutions such as Karman vortex streets
The Navier--Stokes equations are axially symmetric, so with symmetric boundary conditions, how can features such as Karman vortex streets develop?
I understand that in reality symmetry does never ...
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Stable iterative solver for complex symmetric linear systems
I am interested in the iterative solution (preferably Krylov-type solvers) of a problem $\boldsymbol{A}x=b$, with $x,b\in\mathbb{C}^{n\times1}$ and $\boldsymbol{A}\in\mathbb{C}^{n\times n}$. $\...
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Are the eigenvalues of the product matrix of two real symmetric square matrices also real values?
Suppose $A,B \in \mathbb{R}^{n\times n}; A=A^T, B=B^T$, let $C = AB, D =BA$,
If we have all the real eigenvalues of $A$ and $B$, e.g. the eigenvalue decomposition of them:
$A=P\Lambda_1 P^T$,
$B=Q\...
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How property-invariance is imposed to neural nets?
I was wondering how specific symmetries or constraints such as property-invariance transformation are imposed on any (deep) neural net when they are trained.
I'll appreciate it if anyone can aware me ...
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Axisymmetric jet boundary conditions
I am working on analyzing a flow downstream of an axisymmetric jet in a 2D slice i.e, in a rectangle (size L,R) of (z,r) coordinates so that velocity components are (w,v). I am confused about the ...
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Compatibility condition for Poisson equation in cylindrical symmetry
I'm trying to implement multigrid approach for a Poisson equation $\frac{1}{r}\frac{\partial}{\partial r}\left( r \frac{\partial H}{\partial r} \right) = f$ with all Neumann boundary conditions. ...
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Under what specific circumstances can a matrix lose symmetry?
This is a general question: In this blog post, the author points out that under a unitarily invariant norm, the closest symmetric matrix to the square matrix $M$ is $\frac 1 2 (M + M^T)$. The general ...
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