# Questions tagged [orthonormal]

For questions related to orthonormality. A set of vectors in an inner product space is called orthonormal if each vector is a unit vector, and vectors are pairwise orthogonal.

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### Orthonormal Basis of $L^2[0,1]$ having indicator functions?

I was asked to construct an ONB of $L^2[0,1]$ having functions taking at most two values. By suitably scaling, I can think them as indicator functions. So question boils down to finding countably many ...
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### Orthogonal Bases and Fourier Approximation

I am confused about how my professor resolved a fourier approximation. The question was: Find the fourth-order fourier approximation of: $$f(x) = \sin (5x)$$ on the interval: $$0\le x \le 2\pi$$ He ...
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### Existence of a $q$-orthonormal basis of $\mathbb{R}^{r+s}$

For some propositions and proofs it was assumed that there exist a $q$-orthogonal (respect. $q$-orthonormal) basis of $\mathbb{R}^{r+s}\subset Cl_{r,s}$. Here $q$ is a quadratic form. Since we ...
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### Using Gram-Schmidt to extend an orthonormal basis for a subspace

So, given a basis for $V$, I know how to use the Gram-Schmidt process to get an orthonormal basis. My question is, suppose we have an orthonormal basis for a subspace $U$ of $V$. How can we extend ...
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