If $\{ e_1, ..., e_n\}$ is a basis for $V$, show that $\{T(e_1), ..., T(e_n)\}$ is a basis for $W$.
88013
injective linear transformation 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
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
38412
Basis for tensor products
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 $T^n$
76498
Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
124786
Prove that V contains a subspace of each dimension
120535
Basis of the polynomial vector space
158852
If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
150720
Given that $W$ is a subspace of $V$, prove: $\dim W=\dim V \implies W=V$
70475
Proving a basis for inner product space V when $||e_j-v_j||< \frac{1}{\sqrt{n}}$.
52888
Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$
24585
Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
21366
Help on the relationship of a basis and a dual basis
59929
Why is $(e_n)$ not a basis for $\ell_\infty$?
88442
Prove that there's no ordered basis $E$ in which $T{x\choose y}={0\choose y}$ can be represented as $1\ 2\choose 2\ 4$