What are Raina and Jadeja?

Suppose P is the projection matrix onto the subspace S and Q is the projection onto, the orthogonal complement 𝐒^⊥. What are P Q and P Q ? Show that P-Q is its own inverse. | Numerade

Let S be the following subspace of R^4. S spans I, H, H. Give dim(S) and dim(SL). SL is the orthogonal complement of S. (b) Compute Ps and PsL, the projection matrices on S and SL, respectively. What are the relationships between the column spaces and nullspaces of Ps and PsL - i.e., C(Ps), N(Ps), C(Ps-), and N(Ps-). Give orthonormal bases for each of C(Ps), N(Ps), C(Ps1), and N(Ps). Give the eigenvalues of Ps, along with their algebraic and geometric multiplicities.