Given a linear subspaces S 1 , S 2 . . S n ⊆ R d {\displaystyle S_{1},S_{2}..S_{n}\subseteq R^{d}} , find n {\displaystyle n} representatives x i ∈ S i {\displaystyle x_{i}\in S_{i}} such that x i ⊥ x j {\displaystyle x_{i}\perp x_{j}} for all i ≠ j {\displaystyle i\neq j} .
