$T$ is a linear operator on $V$ and fix $v∈ V$...
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.
61931
Positive operator is bounded
45130
Cyclic vector implies commuting linear operator is a polynomial
81040
proof about commutative operators and T-cyclic vectors
87897
Bounded operators on separable Hilbert spaces
144019
A strictly positive operator is invertible
137873
Problems that involves two facts in the definition of vector spaces
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
2439
If a linear operator has an adjoint operator, it is bounded
80279
Show that $S + T$ and $aT$ are linear
45071
Having the derivative be an operator
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
18379
Linear transformation $T:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ such that $T^{2}=\lambda T.$
75855
Show that $\det{(A + sxy^*)}$ is linear in $s$
11159
Problem about a compact operator $T:l^p\rightarrow l^p$
30996
If $\langle Ta, a\rangle \in \mathbb{R}$ for all $a$ then $T$ is self-adjoint