Prove $(\ker T)^\bot = \operatorname{Im}(T^*)$
48291
Proof that $\mathrm{ker}(f^*) = \mathrm{im}(f)^{\perp} $
151721
Uhlmann's Theorem: proof of $\text{tr}(A^{\dagger} B) = \langle m | A \otimes B |m\rangle $
23095
Prove that T is a linear transformation
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
97158
Prove that the operator norm is a norm
117175
Proof that the 2-norm of orthogonal transformation of a matrix is invariant
8374
How to prove that $R/I \otimes_R M \cong M / IM$
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
90475
Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
81040
proof about commutative operators and T-cyclic vectors
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
34700
Proving that the matrix exponential map is surjective onto the general linear group
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
55018
Prove that $A^*A + I$ is invertible
35345
How do i prove invertibility of this linear transformation
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$