# Tagged Questions

**1**

vote

**0**answers

34 views

### Find a common expression (parameterized by y = 1/2, 1 and 2) uniting three (rational) polynomials in k [closed]

I am seeking a common "simple" expression (preferably/presumably a sum of products of linear factors, or sum of products of low-degree factors) uniting the three polynomials (parameterized by ...

**3**

votes

**1**answer

122 views

### Reference for partial Hadamard matrices

Definition. An $m\times n$ matrix is said to be a partial Hadamard matrix (let's say PHM) if its entries are chosen from $\lbrace -1, 1 \rbrace$ such that the dot product of each pair of row vectors ...

**0**

votes

**0**answers

121 views

### Lattice basis reductions and finding minimal values

While reading several articles about lattice basis reduction I am left with a few questions.
For one, I came across this piece of text
Let $\alpha$ and $\beta \in \mathbb{R}$. Also let $X>0$ and ...

**6**

votes

**1**answer

560 views

### Integer solution to special system of linear equations

This problem appear in my research, but I am unable to solve it.
There should be an easy argument, but I have not yet found it.
Informal version
An integer $k\geq 2$ is fixed.
We are given a matrix ...

**2**

votes

**1**answer

175 views

### On solution of a class of discrete-time Lyapunov equation

Hello members, let's consider the following equation
$$X=F_{1}XF_{1}^{T}+...+F_{p}XF_{p}^{T}+C$$
where $p$ is an positive integer and $C$ is a known positive semidefinite matrix. If we augment ...

**2**

votes

**1**answer

124 views

### On solution of a discrete-time equation

Hello, members.
I have a problem for the following problem
when I derive an optimization algorithm for stochastic singular systems
$$S(k+1)=A(k)S(k)A^{T}(k)+R(k)+F(k)S(k+1)F^{T}(k)$$
where ...

**8**

votes

**2**answers

464 views

### Three half circles on the plane may not meet nicely

Let $H$ denote the union of the northen hemisphere of the unit circle $S^{1}$ with the interval $[-1,1]$ on the $x$-axis. That is, $H=\{(x,\sqrt{1-x^{2}}):-1\le x\le 1\}\cup\{(x,0):-1\le x\le 1\}$
...