If $V$ is a vector space, then, proving that...
20879
Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
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 $V$
106670
Existence of vector space complement and axiom of choice
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
74623
Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
4374
Geometric interpretation of a vector space and subspace?
105367
Proving $||\vec{a}+\vec{b}|| = ||\vec{a}-\vec{b}|| \iff \vec{a} \perp \vec{b}$
47015
Vector Space Structures over ($\mathbb{R}$,+)
99300
Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
146143
Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
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
131993
Prove that vector space and dual space have same dimension
124786
Prove that V contains a subspace of each dimension
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
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 $T^n$