query: Suppose $U$ is a subspace of $\mathbb{R}^{4}$ defined by $U =\mathrm{span} \,((1,2,3,-4),(-5,4,3,2))$ Find: orthonormal basis of $U$ and $U^{\perp}$
positive_passages.docid: 148595
positive_passages.text: Find Orthogonal complement
negative_passages.docid: 723
negative_passages.text: Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
negative_passages.docid: 14550
negative_passages.text: Every Hilbert space has an orthonomal basis - using Zorn's Lemma
negative_passages.docid: 123665
negative_passages.text: A question in Subspaces in linear algebra
negative_passages.docid: 73690
negative_passages.text: If $\mathbb R^3\setminus V$ connected where $V$ is the subspace generated by $\{(1,1,1),(0,1,1)\} $
negative_passages.docid: 74623
negative_passages.text: Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
negative_passages.docid: 120535
negative_passages.text: Basis of the polynomial vector space
negative_passages.docid: 73286
negative_passages.text: Show that the set of all symmetric, real matrices is a subspace, determine the dimension
negative_passages.docid: 120610
negative_passages.text: Find a subset of $S = \{(1, 0, i), (i, 2, -3), (2-i, 1+i, i)\}$ that forms a basis for $\textsf V = \operatorname{span}(S)$
negative_passages.docid: 137769
negative_passages.text: How to find a basis for a subspace?
negative_passages.docid: 141794
negative_passages.text: Invariant subspaces of specific dimension
negative_passages.docid: 121047
negative_passages.text: Proof: Sum of dimension of orthogonal complement and vector subspace
negative_passages.docid: 26497
negative_passages.text: Take $\mathbb{R}$ as a vector space over $\mathbb{Q}$, then a basis for $\mathbb{R}$, then $|B|=2^{\aleph_0}$
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 10715
negative_passages.text: Orthogonal projection and two subspaces
negative_passages.docid: 52888
negative_passages.text: Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$