Showing that $\left(\operatorname{Im}\left(T^*\right)\right)^\perp=(\ker T)$ (solution verification)
45998
The range of $T^*$ is the orthogonal complement of $\ker(T)$
138342
Proof of a matrix exponential identity
141286
When is $\mathbf{X}^{T}\mathbf{X}+\lambda\mathbf{I}$ invertible?
124424
How to show that there is a deduction of $\varphi\leftrightarrow\psi$
80996
A canonical construction proving $\left|HK\right| = \left|H\right|\left|K\right| / \left|H \cap K\right|$?
22297
Normal operator $\Rightarrow$ S invariant implies $S^\perp$ invariant
15793
Is the formula $(\text{ker }A)^\perp=\text{im }A^T$ necessarily true?
81868
How to prove $\operatorname{Tr}(AB) = \operatorname{Tr}(BA)$?
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
137209
Finding the Matrix of a Linear Operator Satisfying a Polynomial
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
46669
How can I prove these are the adjoint operators?
2455
Prove that $\left(\sum^n_{k=1}x_k\right)\left(\sum^n_{k=1}y_k\right)\geq n^2$
60514
Isometric  Left Inverse Adjoint
146984
Prove: Full Rank and a solution os linear system
55488
Proving that $\operatorname{codim}(X,Y)=\dim(\mathcal{O}_{X,\eta})$