matrix theory ( ask about proofing the projection.)
Let u be a non-zero vector of an n-dimensional Euclidean space U where n>=2.
show that there exists a basis {y_1,...., y_n} of U such that the projection of y_i on <u> is 2u for i=1,...,n.
Let u be a non-zero vector of an n-dimensional Euclidean space U where n>=2.
show that there exists a basis {y_1,...., y_n} of U such that the projection of y_i on <u> is 2u for i=1,...,n.
thanks first
Choose a basis of the orthogonal complement of , define , and check that it works. You did not ask for an orthogonal basis, did you?