Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Suppose we are given a Riemannian Metric $g$ on $\mathbb{R}^n$. Let $v_1\in\mathbb{R}^n$ with $g(v_1,v_1)=1$. Is it possible to find a base $\{v_1,v_2,...,v_n\}$ of $\mathbb{R}^n$ in such a way that $g(v_i,v_j)=\delta_{ij}$, $\forall\ i,j=1,...,n$ ?

share|improve this question

1 Answer 1

up vote 1 down vote accepted

Yes, the Gram–Schmidt procedure works in any Euclidean space. (From what you write, I assume that by Riemannian metric you mean just a constant inner product on the vector space $\mathbb{R}^n$, not an inner product that varies from point to point on the manifold $\mathbb{R}^n$.)

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.