Intereting Posts

$\lim_{x\to 1^-} \sum_{k=0}^\infty \left( x^{k^2}-x^{(k+\alpha)^2}\right)$
Integration method for $\int_0^\infty\frac{x}{(e^x-1)(x^2+(2\pi)^2)^2}dx=\frac{1}{96} – \frac{3}{32\pi^2}.$
Card passing game, maximum length
How can we determine the closed form for $\int_{0}^{\infty}{\ln(e^x-1)\over e^x+1}\mathrm dx?$
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
Prime number between $n$ and $n!+1$
Cofinite\discrete subspace of a T1 space?
Measure on topological spaces
looking for materials on Martin Axiom
A question about intersection number
Is there an element with no fixed point and of infinite order in $\operatorname{Sym}(X)$ for $X$ infinite?
Shouldn't this function be discontinuous everywhere?
$f(x^2) = 2f(x)$ and $f(x)$ continuous
Find $C$ such that $x^2 – 47x – C = 0$ has integer roots, and further conditions
Is there a meaningful distinction between “inclusion” and “monomorphism”?

If I have a set of matrices, call this set U, how can I make this a UFD (unique factorization domain)? In other words, given any matrix $X \in U$, I would be able to factorize X as $X_1 X_2 … X_n$ where $X_i \in U$ and this factorization is unique?

We may assume the matrix entries are real or complex, but I’d prefer not to add additional restrictions on the numbers.

I guess there are many ways to do this, trivially I can take the set $\{pI\}$ where $I$ is the identity matrix and $p$ is a prime number. But I want to have matrices that are more “general”. Thanks!

- Enlightening proof that the algebraic numbers form a field
- $1+a$ and $1-a$ in a ring are invertible if $a$ is nilpotent
- Tensor product algebra $\mathbb{C}\otimes_\mathbb{R} \mathbb{C}$
- Why is there a $p\in \mathbb{N}$ such that $mr - p < \frac{1}{10}$?
- How to prove that a complex number is not a root of unity?
- When $\Bbb Z_n$ is a domain. Counterexample to $ab \equiv 0 \Rightarrow a\equiv 0$ or $b\equiv 0\pmod n$

Edit: There would be a distinguished subset $P \subset U$ which are “primes”. To rephrase the question: what I want is, if I take a bunch of elements $X_i, Y_i \in P$, I can guarantee that $\prod X_i \neq \prod Y_i$, if at least there exists one $X_j \neq Y_j$. Can it be done?

Some of the matrices must be non-commutative, ie $A,B \in P$ and $AB \neq BA$.

- The sum of three colinear rational points is equal to $O$
- Pseudo-inverse of a matrix that is neither fat nor tall?
- prove that projection is independent of basis
- How to show the intersection of a prime ideal and a subring is a prime ideal
- Linear algebra doubt about the use of the word 'finite'
- Derivative of conjugate transpose of matrix
- $M \oplus M \simeq N \oplus N$ then $M \simeq N.$
- Minimum eigenvalue and singular value of a square matrix
- Maximizing the trace
- Dot product for 3 vectors

- Proving that a compact subset of a Hausdorff space is closed
- Calculating the max and min of $\sin(x)+\sin(y)+\sin(z)$
- How to prove $\lim_{n\rightarrow \infty} {a^n \over n!}=0$
- Probability of $(a+b\omega+c\omega^{2})(a+b\omega^{2}+c\omega)=1$
- a simple recurrence problem
- Proof that $\sum_{i=1}^n{1} = n$ for all $n \in \Bbb Z^+$
- math-biography of mathematicians
- Sequence $a_k=1-\frac{\lambda^2}{4a_{k-1}},\ k=2,3,\ldots,n$.
- What really is ''orthogonality''?
- A question on the Stirling approximation, and $\log(n!)$
- computing ${{27^{27}}^{27}}^{27}\pmod {10}$
- Why would some elementary number theory notes exclude 0|0?
- If $ab=ba$, Prove $a^2$ commutes with $b^2$
- How many integers between have digit sum 20?
- $\mathbb{Z} \times \mathbb{Z}$ is cyclic.