query: Orthonormal set in $L^2(0,1)$ that is not complete
positive_passages.docid: 141917
positive_passages.text: Rademacher functions form an orthonormal system but not an orthonormal basis
negative_passages.docid: 158852
negative_passages.text: If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
negative_passages.docid: 6319
negative_passages.text: Finding an orthonormal basis for a matrix
negative_passages.docid: 143642
negative_passages.text: Does the sequence $(\sqrt{n} \cdot 1_{[0, 1/n]})_n$ converge weakly in $L^2$?
negative_passages.docid: 81229
negative_passages.text: Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
negative_passages.docid: 140225
negative_passages.text: Linear transformation maps the first quadrant to a closed set
negative_passages.docid: 63529
negative_passages.text: How to show that this set is compact in $\ell^2$
negative_passages.docid: 149997
negative_passages.text: Convolution operator has norm 1 with respect to $L^2$ norm
negative_passages.docid: 151719
negative_passages.text: Connected set in $\mathbb{S}^1$
negative_passages.docid: 134575
negative_passages.text: Show that the mapping $f → f~'$ from $C^1([0 , 1])$ to $C([0 , 1])$ is not continuous.
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: 93177
negative_passages.text: in which subset of $R^2$ the series is convergent?
negative_passages.docid: 39430
negative_passages.text: Orthogonal matrix and orthonormal columns
negative_passages.docid: 127882
negative_passages.text: Proofs involving orthonormal basis
negative_passages.docid: 50946
negative_passages.text: Separable Hilbert space have a countable orthonormal basis
negative_passages.docid: 149219
negative_passages.text: If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
negative_passages.docid: 154621
negative_passages.text: A set with a finite integral of measure zero?