Proving that {$v, T(v), ..., T^{n-1}(v)$} is a basis of $ V $
114309
T-invariant linear independence
153406
$[F(t):F(t^n)]=n$ where $t$ is trascendental
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
144531
How to prove that a nilpotent operator has a basis representation that is strictly upper triangular?
20110
How to prove $(AB)^T=B^T A^T$
81040
proof about commutative operators and T-cyclic vectors
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
95379
Prove that $V = V_1 \oplus V_2$ in the following
123275
Prove $[A,B^n] = nB^{n-1}[A,B]$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
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?
120766
Prove ${y_n}$ is a basis for a Hilbert space $H$.
52596
A basis for $k(X)$ regarded as a vector space over $k$
57037
How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
3846
Let $v_{1}=(1,-2,3),v_{2}=(0,-1,2)$. Enlarge $\{v_{1},v_{2}\}$ to a basis for $\mathbb{R}^3$.
49296
Prove $|(1+|u|^2)v-(1+|v|^2)u|>|u\bar{v}-\bar{u}v|$