We aim to construct an orthogonal matrix Q that transform a given column of A-call itx into the corresponding column of R-call it y. For this we found ‖x‖ =‖Qx‖ =‖y‖.We extended the notation of orthogonal projection that we explained it we also discussed only projection onto a single vector (or, equivalently,the one dimensional subspace spanned by that vector).We saw that we can find the analogous formulas for projection onto a plane in 〖IR.〗^3The orthogonality is becoming an important mathematical tools in linear algebra, there are many ways of constructing new cods from old ones.Here ,we consider one of the most.

Orthogonality , orthogonal matrix , Dual Code Application , orthogonal projection .