query: Does every infinite-dimensional inner product space have an orthonormal basis?
positive_passages.docid: 144151
positive_passages.text: An orthonormal set cannot be a basis in an infinite dimension vector space?
negative_passages.docid: 32420
negative_passages.text: A complete orthonormal system contained in a dense sub-space.
negative_passages.docid: 61484
negative_passages.text: Continuously invertible operators
negative_passages.docid: 88153
negative_passages.text: Finding all inner products on $\mathbb{R}^2$ for which a given linear map is orthogonal
negative_passages.docid: 78654
negative_passages.text: An example of a norm which can't be generated by an inner product
negative_passages.docid: 83360
negative_passages.text: The completion of a separable inner product space is a separable Hilbert space
negative_passages.docid: 141456
negative_passages.text: Why is it important that a basis be orthonormal?
negative_passages.docid: 103142
negative_passages.text: Question on equivalence of inner product
negative_passages.docid: 57619
negative_passages.text: Norms Induced by Inner Products and the Parallelogram Law
negative_passages.docid: 87580
negative_passages.text: Canonical examples of inner product spaces that are not Hilbert spaces?
negative_passages.docid: 154628
negative_passages.text: What should we understand from the definition of orthogonality in inner product spaces other than $\mathbb R^n$?
negative_passages.docid: 134162
negative_passages.text: What is a basis for the space of $n\times n$ Hermitian matrices?
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 152742
negative_passages.text: Finding a basis of an infinite-dimensional vector space?
negative_passages.docid: 60934
negative_passages.text: What is a complex inner product space "really"?
negative_passages.docid: 151425
negative_passages.text: Does $\mathbb{R}^n$ have a real vector space structure with dimension other than $n$?
negative_passages.docid: 19729
negative_passages.text: An infinite dimensional limit