The symmetry tag has no usage guidance.

**9**

votes

**0**answers

100 views

### What is the symmetry group fixing norms of elements of a unitary matrix?

Let $N\geq1$ be an integer and let us say that two matrices $U,V\in U(N)$ are related if $|U_{ij}|=|V_{ij}|$ for all indices $1\leq i,j\leq N$.
When exactly are two unitary matrices related in this ...

**6**

votes

**0**answers

127 views

### Symmetry of function defined by integral

(Originally posed in Math.SE in Jan 2013. Received no complete answers as of yet.)
Define a function $f(\alpha, \beta)$, $\alpha \in (-1,1)$, $\beta \in (-1,1)$ as
$$ f(\alpha, \beta) = \int_0^{\...

**3**

votes

**0**answers

188 views

### Find the axis of symmetry in a point cloud

I have some dataset which describes a spherical cloud of points in 4D space. Actually, the coordinates of the points are the coefficients of unit quaternions, so you get the idea on what the data is ...

**2**

votes

**0**answers

154 views

### Diffeomorphism between open annuli preserving common symmetries

Suppose $A$ and $B$ are subsets of $\mathbb{R}^2$ homeomorphic (and thus $C^\infty$ diffeomorphic) to the open annulus (punctured $\mathbb{B}^2$) and let $G$ be the group of isometries of ${\mathbb R}^...

**1**

vote

**0**answers

70 views

### Semiflows and continuous symmetries

Given a differential equation on a Banach space $\mathcal{X}$ of the form $\frac{d u}{d t} = F(u)$, it is often the case that $F$ is equivariant under translations, i.e. that $T_\alpha F(u) = F(T_\...

**0**

votes

**0**answers

80 views

### “Box Nodes” in Directed Graphs with Paired IO Symmetry

Consider directed graphs where all nodes have 2 inputs and 2 outputs. If we
design a box with N inputs and N outputs, what is the smallest number of
nodes it must contain to satisfy “pair symmetry” (...

**0**

votes

**0**answers

47 views

### Using symmetries of a r.v.'s distribution to boost samples and possibly do variance reduction

Suppose, for example, you are simulating samples from a (multivariate) Gaussian with mean zero and covariance $\Gamma=BB^T$. If you had generated a sample $x$, you could generate more (dependent) ...