Finite Dimensional Vector Space proof: No linear maps such that $PQ-QP=I$
7622
$AB-BA=I$ having no solutions
41520
Prove that $L(V,W)$ forms a vector space
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
19415
Proof that every finite dimensional normed vector space is complete
151354
Why are there no non-trivial regular maps $\mathbb{P}^n \to \mathbb{P}^m$ when $n > m$?
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
107389
Show that the vector space of real functions is not finitely spanned
108742
Proving commutativity of addition for vector spaces
91022
How do I prove that a subspace of a vector space $X$ is the null space of some linear functional on $X$?
151425
Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
69206
A finite-dimensional vector space cannot be covered by finitely many proper subspaces?
137873
Problems that involves two facts in the definition of vector spaces
124786
Prove that V contains a subspace of each dimension
54875
How to prove polynomials with degree $n$ does not form a vector space?
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
29655
$L^p$ and $L^q$ space inclusion