Reading a basis for $\operatorname{Null}(A)$ and $\operatorname{Null}(A^T)$ from the reduced row-echelon form of $A$
113987
Kernels and reduced row echelon form - explanation
5506
Perturbation property of Orthonormal basis for Hilbert space
119352
compact and self adjoint square root of an operator
112939
Find a basis for the subspace of $\mathbb{R}^4$ spanned by the given vectors.
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
93550
How to find the matrix representation of an operator from its action on a basis?
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
44927
Finding rank-nullity of a given matices
134999
Writing empty set as union of basis elements for a topology.
137769
How to find a basis for a subspace?
109471
The eigenvectors of the transpose operator
32833
Matrix is either null or similar to the elementary matrix $E_{2,1}$
87254
The computation of nullity and rank of a linear transformation.
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
59804
Show that the plane $\{su+tv|s,t \in\Bbb R\}$ in $\Bbb R^3$ is equal to the null space of some element of $(\Bbb R^3)^{*}$.
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$