Dual vector space properties ($\forall \phi\in E^*,\langle\phi,x\rangle=0\implies x=0$)
119947
Can a non-zero vector have zero image under every linear functional?
48563
If $\Gamma^k_{ij}(p)=0$, then $\nabla_{E_i}E_j (p)=0?$
51483
Prove: If a linear map, $φ: U→V$ is bijective, then $φ(x)=0$ has only the solution $x=0$.
60685
The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
32896
Vector spaces for the irreducible representations of the Lorentz Group
41520
Prove that $L(V,W)$ forms a vector space
74884
Tensor product in dual-space
116112
Examples of 'almost' vector spaces where unitary law fails
81229
Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
146339
Proof of -(-v)=v in a vector space
102371
Proving that two vector spaces of equal dimension are isomorphic
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
89089
Prove that there is a unique inner product on $V$
144019
A strictly positive operator is invertible
105014
Is the zero vector in $\mathbb{R}^n$ by itself a subspace of $\mathbb{R}^n$?
129810
What kind of vector spaces have exactly one basis?
66283
Let V be a vector space. If every subspace of V is T-invariant, prove that there exist a scalar multiple c such that T=c1v