For any $n ≥ 2$, there exists a $n × n$ real matrix $A$ such that the set $\{A^p | p ≥ 1\}$ spans the $\Bbb R$-vector space $M_n(\Bbb R)$.
34372
Are $10\times 10$ matrices spanned by powers of a single matrix?
4776
Prove that the power set of an $n$-element set contains $2^n$ elements
43504
Proving the existence of a complement subspace $U' \subset V$.
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
37953
Primary Decomposition of $\mathbb{R^n}$ under T
42883
Cross product in $\mathbb R^n$
100726
Prove that the set of powers of a set, $\{ A^n : n \in \mathbb{N} \}$ exists by using ZFC axioms (without replacement).
122121
Is there a vector space that cannot be an inner product space?
86362
Cyclic vectors in a real vector space
68490
For $x\in\mathbb R\setminus\mathbb Q$, the set $\{nx-\lfloor nx\rfloor: n\in \mathbb{N}\}$ is dense on $[0,1)$
123505
how to prove vector norm equivalence in finite dimensional space($\mathbb{R}^{n}$)?
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
11817
Proving that every set $A \subset \Bbb N$ of size $n$ contains a subset $B \subset A$ with $n | \sum_{b \in B} b$
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
40409
If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
49087
Show that a norm on an inner product space satisfies parallelogram law.