On a : $\ds X = \begin{pmatrix} x_{1} \\ \vdots \\ x_{n} \end{pmatrix} \in \mathcal{H}$ si et seulement si : $$\ds\left\langle \begin{pmatrix} a_{1,1} \\ \vdots \\ a_{1,n} \end{pmatrix} , \begin{pmatrix} x_{1} \\ \vdots \\ x_{n} \end{pmatrix} \right\rangle =\dots=\left\langle \begin{pmatrix} a_{p,1} \\ \vdots \\ a_{p,n} \end{pmatrix},\begin{pmatrix} x_{1} \\ \vdots \\ x_{n} \end{pmatrix}\right\rangle =0$$ $$\ds X\in\mathrm{Vect}\left(\begin{pmatrix} a_{1,1} \\ \vdots \\ a_{1,n} \end{pmatrix},\dots,\begin{pmatrix} a_{p,1} \\ \vdots \\ a_{p,n} \end{pmatrix}\right)^{\perp}$$ donc : $$\mathcal{H}^{\perp} = \mathrm{Vect}\left(\begin{pmatrix} a_{1,1} \\ \vdots \\ a_{1,n} \end{pmatrix},\dots,\begin{pmatrix} a_{p,1} \\ \vdots \\ a_{p,n} \end{pmatrix}\right)$$