If $W\subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite dimensiona
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
51397
If a field $F$ is such that $\left|F\right|>n-1$ why is $V$ a vector space over $F$ not equal to the union of $n$ proper subspaces of $V$
67191
When is the union of a family of subspaces of a vector space also a subspace?
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
14429
dimension of a subspace spanned by two subspaces
38516
Show a subset is subspace of a vectorspace and find the dimension
28238
A question about long exact sequence of finite dim vector spaces
125623
Subspaces of separable normed spaces
152325
Every subspace of the dual of a finite-dimensional vector space is an annihilator
73773
$C(M)=\{A\in M_n(\mathbb{C}) \mid AM=MA\}$ is a subspace of dimension at least $n$.
53971
If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
81471
Finite dimensional spaces
35305
Why is $\mathbb{R}^2$ not a subset and /or a subspace of $\mathbb{R}^3$?
106487
Let $S$ and $W$ be subsets of a vector space $V$. Show that if $S$ is a subset of $W$, then $\mathrm{span}(S)$ is a subspace of $\mathrm{span}(W)$
45485
Dimension of a subset
22295
Subspace of a separable space is separable
73690
If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $