Suppose $\dim V >\dim W$. Then no linear map from $V$ to $W$ is injective
94165
Why is a map to a smaller dimensional space not injective?
139176
The real line is not homeomorphic to any non-trivial product space
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
125184
Why $\dim(\hom(V,W))=\dim(V) * \dim(W)$?
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
122121
Is there a vector space that cannot be an inner product space?
85032
$Q(\mathbb{Z}[t]) / \mathbb{Z}[t]$ is not injective
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
53364
dim$(V)$ = $n$, dim$(W)$ = $m$ $\implies$ dim($L(V,W)$) = $nm$
33129
A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
20284
Continuous injective map is strictly monotonic
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
25874
Showing that a certain map is not flat by explicit counterexample
117131
Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
121198
$W^{1,1}(\mathbb{R}^n)$ is not compactly embedded in $L^1(\mathbb{R}^n)$?
78344
Nonconstant linear functional on a topological vector space is an open mapping
28238
A question about long exact sequence of finite dim vector spaces