Considering ${\displaystyle \mathbf {A} }$ is a Matrix of reals, is possible to define the kernel space, for example:

${\displaystyle {\mbox{N}}(\mathbf {A} )={\mbox{Null}}(\mathbf {A} )={\mbox{Ker}}(\mathbf {A} )=\left\{{\textbf {x}}\in \mathbb {R} ^{n}:\mathbf {A} {\textbf {x}}={\textbf {0}}\right\}{\text{,}}}$

In the case the matrix ${\displaystyle \mathbf {A} (\mathbf {q} )}$ is a function, the kernel space is in general different for each value of q, but ic can be defined a generalized kernel space:

${\displaystyle {\mbox{genN}}(\mathbf {A} (\mathbf {q} ))={\mbox{genNull}}(\mathbf {A} (\mathbf {q} ))={\mbox{genKer}}(\mathbf {A} (\mathbf {q} ))=\left\{{\textbf {x}}\in \mathbb {R} ^{n}:\mathbf {A} (\mathbf {q} ){\textbf {x}}={\textbf {0}}\forall \mathbf {q} \right\}{\text{,}}}$