query: theorem of existence of an orthogonal complement
positive_passages.docid: 24585
positive_passages.text: Proving that $\mathbf{W}$+$\mathbf{W^{\perp}}$=$\mathbb{R^{n}}$
negative_passages.docid: 48579
negative_passages.text: How to find the orthogonal complement of a subspace?
negative_passages.docid: 14048
negative_passages.text: Proof that the complement of zero-measure set on $[0,1]$ is dense in $[0,1]$
negative_passages.docid: 63465
negative_passages.text: Orthogonal Projection of $ z $ onto the Affine set $ \left\{ x \mid A x = b \right\} $
negative_passages.docid: 45998
negative_passages.text: The range of $T^*$ is the orthogonal complement of $\ker(T)$
negative_passages.docid: 109046
negative_passages.text: Is the complement of an open ball in a Banach space connected?
negative_passages.docid: 93165
negative_passages.text: A projection satisfying $\| Px \| \leq \|x\|$ for all $x$ is an orthogonal projection
negative_passages.docid: 59531
negative_passages.text: Do $T$-invariant subspaces necessarily have a $T$-invariant complement?
negative_passages.docid: 48524
negative_passages.text: Existence proof of the tensor product using the Adjoint functor theorem.
negative_passages.docid: 4151
negative_passages.text: Every subspace of a vector space has a complement
negative_passages.docid: 21459
negative_passages.text: Orthogonal complement examples
negative_passages.docid: 62077
negative_passages.text: Prove that if $W_1\subseteq V$ finite-dimensional, then there is $W_2\subseteq V$ such that $V=W_1\oplus W_2$
negative_passages.docid: 99221
negative_passages.text: Orthogonality lemma sine and cosine
negative_passages.docid: 103923
negative_passages.text: Double orthogonal complement is equal to topological closure
negative_passages.docid: 118996
negative_passages.text: Prove that $T$ is an orthogonal projection
negative_passages.docid: 97994
negative_passages.text: Orthogonality Relations Exercise, Brezis' Book Functional Analysis
negative_passages.docid: 153355
negative_passages.text: Given $S \in B(Y^{*}, X^{*})$, does there exist $T\in B(X,Y)$ such that $S=T^{*}$?