# Thread: How to construct a perpendicular vector w.r.t a bunch of known vectors??

1. ## How to construct a perpendicular vector w.r.t a bunch of known vectors??

Hi,

Given several vectors, which may be or not be orthogonal to each other, how to construct a vector perpendicular to them? In a sense of inner production being zero.

To be specific, I have $n$ vectors $v_{N}$ of length $N$, where $n. So the maximum rank for these vectors is $n$, which leaves space for new vectors perpendicular to all of them. How to construct such a vector? I know Gram-Schmidt process, but it seems it's not what I want.

Thanks.

2. ## Re: How to construct a perpendicular vector w.r.t a bunch of known vectors??

I doubt whether any other process can make a more effective use of Hilbert space structure.