The notes consist of a study of special Lagrangian linear subspaces. We will give a condition for the graph of a linear symplectomorphism $f:({ℝ}^{2n},\sigma ={\sum }_{i=1}^{n}d{x}_i\wedge d{y}_i)\to ({ℝ}^{2n},\sigma )$ to be a special Lagrangian linear subspace in $({ℝ}^{2n}\times {ℝ}^{2n},\omega =\pi *₂\sigma -\pi *₁\sigma )$. This way a special symplectic subset in the symplectic group is introduced. A stratification of special Lagrangian Grassmannian $S{\Lambda }_{2n}\simeq SU\left(2n\right)/SO\left(2n\right)$ is defined.

We construct a family of Lagrangian submanifolds in the complex sphere which are foliated by $(n-1)$-dimensional spheres. Among them we find those which are special Lagrangian with respect to the Calabi-Yau structure induced by the Stenzel metric.