New posts in Vector Spaces

Show for isometry $T:V \rightarrow V$, $\frac{1}{n}\sum_{i=0}^{n-1} T^i$ converges to the orthogonal projection on $ker(T-I)$.

Is every vector subspace also affine?

Prove $R(a \times b) = Ra \times Rb$ given $R \in \mathcal{SO}(3)$ and $a,b \in \mathbb{R}^3$.

Angle between a vector and cross product of two vectors

1-Torus as finite dimensional $\mathbb{R}$-vector space is one dimensional, yet not isomorphic to $\mathbb{R}$

Turning an Abelian Group into a Vector Space

Proof verification: if $W_1 \subseteq W_2$ then $\dim(W_1) \le \dim(W_2)$

Is every $1$-dimensional vector space a field?

Tensor Product with Trivial Vector Space

How to show that $f:V\to V$ is linear?