Show that space of all linear transformations from $V \to V$ is a vector space
41520
Prove that $L(V,W)$ forms a vector space
120535
Basis of the polynomial vector space
93121
How to prove there exists a linear transformation?
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
23372
Show that for an invertible matrix, the images of a set of vectors spanning the space also form a spanning set
141843
n-dimensional vector space isomorphic to the n-th product of a field as abelian groups
121636
General linear group of a vector space
5347
Using the definition of a vector space to prove that $0x = 0$ and $(-1)x = -x$
74465
One-dimensional vector space and it's subspaces
107389
Show that the vector space of real functions is not finitely spanned
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
98759
Proof of "Dual normed vector space is complete"
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
151117
Are all fields vector spaces?
112024
Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)