query: Normed, Finite Dimensional Vector Space are Complete
positive_passages.docid: 19415
positive_passages.text: Proof that every finite dimensional normed vector space is complete
negative_passages.docid: 43431
negative_passages.text: Show that $F+G$ is closed when $G$ a closed subspace of normed space $E$ and $F$ a finite dimensional subspace of $E$.
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 152196
negative_passages.text: About inner products, norms and metrics
negative_passages.docid: 81229
negative_passages.text: Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
negative_passages.docid: 26989
negative_passages.text: Show that C[0,1] is a vector space
negative_passages.docid: 113326
negative_passages.text: Proving orthogonality of vectors in a complex vector space
negative_passages.docid: 49087
negative_passages.text: Show that a norm on an inner product space satisfies parallelogram law.
negative_passages.docid: 116823
negative_passages.text: VERIFYING: Proving an $n \times n$ Matrix Vector Space
negative_passages.docid: 132641
negative_passages.text: Proving that Euclidean Space is a complete metric space
negative_passages.docid: 125073
negative_passages.text: Finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 89058
negative_passages.text: Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
negative_passages.docid: 29030
negative_passages.text: Vector space with new scalar multiplication defined over finite field still vector space?
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 83360
negative_passages.text: The completion of a separable inner product space is a separable Hilbert space
negative_passages.docid: 124959
negative_passages.text: Does weak compactness imply boundedness in a normed vector space (not necessarily complete)?
negative_passages.docid: 43503
negative_passages.text: Bases of complex vector spaces and the axiom of choice