I have a homogeneous problem with the form $\mathbf{A}_{n\times6}\mathbf{x}_{6\times1}=\mathbf{0}_{n\times1}$ in which the columns of the $\mathbf{A}$ are orthogonal in each row, for example
$\mathbf{A}=\left[ \begin{matrix} \vdots & \vdots \\ {{\mathbf{a}}_{i}^T} & {{\mathbf{b}}_{i}}^T \\ \vdots & \vdots \\ \end{matrix} \right]$
with, $\mathbf{a}_{i}^{T}{{\mathbf{b}}_{i}}=0$ for each row in $\mathbf{A}$. This results in a
$\mathbf{N}={{\mathbf{A}}^{T}}\mathbf{A}=\left[ \begin{matrix} 1 & 0 & 0 & 0 & 0 & -1 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 & 1 & 0 \\ -1 & 0 & 0 & 0 & 0 & 1 \\ \end{matrix} \right]$
This structure is unique and results in three non-zero singular values out of six.
I am finding it hard to understand the geometric meaning of this problem and would appreciate any help or direction (literature) to understand it.