Intereting Posts

Upper bound of $a_{n+1}=a_n + \frac{1}{a_n}$
Density of $\mathbb{Q}^n$ in $\mathbb{R}^n$
Order of growth of the entire function $\sin(\sqrt{z})/\sqrt{z}$
Isomorphism between dual space and bilinear forms
Proving that $a,n$ and $b, n$ relatively prime implies $ab,n$ relatively prime
Help on solving an apparently simple differential equation
Hilbert spaces and unique extensions of linear functions.
Showing that $|f(z)| \leq \prod \limits_{k=1}^n \left|\frac{z-z_k}{1-\overline{z_k}z} \right|$
Proof that continuous partial derivatives implies differentiability
Incorrect General Statement for Modulus Inequalities
Every order topology is regular (proof check)
Prime dividing the binomial coefficients
Can “being differentiable” imply “having continuous partial derivatives”?
The elliptic curve $y^2 = x^3 + 2015x – 2015$ over $\mathbb{Q}$
Integrability of Derivative of a Continuous Function

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!

- Completion as a functor between topological rings
- Complete set of equivalence class representative
- If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
- Definition of group action
- Smooth manifold $M$ is completely determined by the ring $F$.
- Hopkins-Levitzki: an uncanny asymmetry?

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 $AB \neq BA$.

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- Eigen Values Proof
- invertible if and only if bijective
- Ideals of Polynomial Rings and Field Extensions
- Geometry question pertaining to $4$ points in the plane where $90$ degree projectors are on each point and we must illuminate the whole plane.
- $|G|>2$ implies $G$ has non trivial automorphism
- Only two groups of order $10$: $C_{10}$ and $D_{10}$
- give a counterexample of monoid
- Adjoining to a ring
- Linear algebra problem from dummite & foote

- Point Group of a pattern
- Isolated singularities of the resolvent
- On Groups of Order 315 with a unique sylow 3-subgroup .
- Normal numbers are meager
- Homeomorphism that maps a closed set to an open set?
- A function which is continuous in one variable and measurable in other is jointly measurable
- $a^m+k=b^n$ Finite or infinite solutions?
- Setting up integral in polar coordinate for surface area of paraboloid
- Some pecular fractional integrals/derivatives of the natural logarithm
- Partial Simplified Proof for the prime version of the Catalan Conjecture
- For which natural numbers $n$ is $\sqrt n$ irrational? How would you prove your answer?
- Inverse of composition of relation
- What's the history of the result that $p_{n+1} < p_n^2$, and how difficult is the proof?
- Two simple series
- Conditional probability independent of one variable