Let $A$ be a matrix, how to show that the left null space of $A$ is the orthogonal complement of the column space of $A$?
114524
Proof Verification: the orthogonal complement of the column space is the left nullspace
126747
Null space for $AA^{T}$ is the same as Null space for $A^{T}$
72560
Eigenspace of the companion matrix of a monic polynomial
64353
Does the set of matrix commutators form a subspace?
86875
Finding the null space of symmetric matrix generated by outer product
61274
If $AA^T$ is the zero matrix, then $A$ is the zero matrix
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
123665
A question in Subspaces in linear algebra
69497
Show that the set of all $n \times n$ orthogonal matrices, $O(n)$, is a compact subset of $\mbox{GL} (n,\mathbb R)$
10715
Orthogonal projection and two subspaces
134162
What is a basis for the space of $n\times n$ Hermitian matrices?
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
113779
If $P$ is an orthogonal matrix its columns form an orthonormal set.
117175
Proof that the 2-norm of orthogonal transformation of a matrix is invariant
1475
In an incomplete inner product space, is a closed linear subspace equal to the orthogonal complement of its orthogonal complement?
17430
If $\operatorname{rank}\left( \begin{bmatrix} A &B \\ C &D \end{bmatrix}\right)=n$ prove that $\det(AD)=\det(BC)$
33188
Dimension of null space of a given problem