Daniel Akech Thiong's user avatar
Daniel Akech Thiong's user avatar
Daniel Akech Thiong's user avatar
Daniel Akech Thiong
  • Member for 9 years, 8 months
  • Last seen this week
16 votes

Proof that the set of irrational numbers is dense in reals

12 votes

If $A$ is a subset of $B$, then $\sup A \leq \sup B$

11 votes
Accepted

Proof that Every Positive Operator on V has a Unique Positive Square Root

8 votes

Prove that 10101...10101 is NOT a prime.

7 votes

When $|G|=105$ and has a normal Sylow $3-$subgroup, then $G$ is abelian.

6 votes

No simple group of order 2016

6 votes
Accepted

Unit Plus Nilpotent Is Unit

5 votes
Accepted

Example of a UFD that is not Dedekind

4 votes

every finite integral domain is a field

4 votes

Let $A$ be any matrix. How do I prove that $\mathrm{Im}(A)=\mathrm{Im}(AA^T)$?

4 votes

Adjoint of Derivative Operator

4 votes
Accepted

Let $N \unlhd G$ where $G$ is a finite group. Prove that order of $ gN$ divides order of $g \; \forall \; g \in G$

4 votes
Accepted

Prove by induction that $\bigg \vert\prod_{k=1}^{n} a_k - \prod_{k=1}^{n} b_k \bigg \vert \leq \sum_{k=1}^{n} | a_k - b_k|$.

3 votes
Accepted

prove that if $ T^2=T $ then T is diagonalizable operator ( over finite dimension vector space)

3 votes

If $f$ is continuous and $f(x+y) = f(x)+f(y)$, then $f(x) = cx$ for all $x \in \mathbb{R}$

3 votes
Accepted

why the Eigen values of given matrix P are of modulus $1$?

3 votes

Let $A\in M_{n,n}(\mathbb{C})$ be a diagonalisable matrix. Prove $\exists B \in M_{n,n}(\mathbb{C})$ such that $B^{2016} = A$

3 votes
Accepted

How do I show that commuting matrices preserve generalized eigenspaces?

3 votes

How do I prove that these two numbers are the only eigenvalues?

3 votes

If $G$ is a group of order $4n+2$, then $G$ contains a subgroup of order $2n+1$

3 votes

Prove that $\{\mathbb e^{r_1x}, \mathbb e^{r_2x}..., \mathbb e^{r_nx}\}$ is linear independent

3 votes

Show $H_n$ is a subgroup of $G$ for any $n\in\mathbb N$

3 votes
Accepted

Inequality $( \sum_{i=1}^{n} a_i)( \sum_{i=1}^{n} \frac{1}{a_i})\geq n^2$

3 votes
Accepted

How to show Cantor function is uniformly continuous?

3 votes

Prove that no group of order $p^2q$ is simple where $p$ and $q$ are prime

3 votes
Accepted

Proving $\frac{|f'(z)|}{1-|f(z)|^2}\leq\frac{1}{1-|z|^2}$ from the Schwarz--Pick Lemma without using other inequality

2 votes
Accepted

Converse of density theorem for $L^1(\Omega)$

2 votes

Show that $\ker(\phi)$ is a maximal ideal if and only if $B$ is a field

2 votes

How to prove $\dim(U)=\dim(W)=\dim(V)-1 \implies V=U+W$ based on the following assumption?

2 votes
Accepted

Is it true that $\det A=\det A^*$?

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