query: Dual space of finite dimensional space V has the same dimension
positive_passages.docid: 143517
positive_passages.text: Isomorphisms Between a Finite-Dimensional Vector Space and its Dual
negative_passages.docid: 69893
negative_passages.text: An inner product space and its proper closed subspace with trivial orthogonal complement
negative_passages.docid: 38033
negative_passages.text: A surjective linear map into a finite dimensional space is open
negative_passages.docid: 98759
negative_passages.text: Proof of "Dual normed vector space is complete"
negative_passages.docid: 15839
negative_passages.text: equivalent norms in Banach spaces of infinite dimension
negative_passages.docid: 107000
negative_passages.text: Dimension of intersection of distinct subspaces
negative_passages.docid: 77175
negative_passages.text: Proof that two spaces that are homotopic have the same de Rham cohomology
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: 99350
negative_passages.text: Are two norms equivalent if they induce the same topology on a vector space?
negative_passages.docid: 134065
negative_passages.text: A question about an $n$-dimensional subspace of $\mathbb{F}^{S}$.
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
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: 59647
negative_passages.text: Vector spaces with fractional dimension
negative_passages.docid: 127795
negative_passages.text: $L^1(μ)$ is finite dimensional if it is reflexive
negative_passages.docid: 88728
negative_passages.text: Dimensions of vector subspaces in a direct sum are additive
negative_passages.docid: 70785
negative_passages.text: A finite Hausdorff space is discrete
negative_passages.docid: 63104
negative_passages.text: Dual cone of $K = \{(x,t) \mid \| \boldsymbol{x} \|_1 \le t \}$