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

2. Originally Posted by lekge
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 $\displaystyle (e_1,\ldots,e_{n-1})$ of the orthogonal complement of $\displaystyle \langle u\rangle$, define $\displaystyle (y_1,\ldots,y_n)=(2u,e_1+2u,\ldots,e_{n-1}+2u)$, and check that it works. You did not ask for an orthogonal basis, did you?