query: Explain whether “unordered” bases and “distinct” bases of a vector space meaning same thing?
positive_passages.docid: 28402
positive_passages.text: Number of bases of an n-dimensional vector space over q-element field.
negative_passages.docid: 99350
negative_passages.text: Are two norms equivalent if they induce the same topology on a vector space?
negative_passages.docid: 98759
negative_passages.text: Proof of "Dual normed vector space is complete"
negative_passages.docid: 94844
negative_passages.text: Unitary map between sets of vectors
negative_passages.docid: 123408
negative_passages.text: Why a subspace of a vector space is useful
negative_passages.docid: 146339
negative_passages.text: Proof of -(-v)=v in a vector space
negative_passages.docid: 61220
negative_passages.text: What does "$\mathbb{F^n}$ is a vector space over $\mathbb{F}$" mean?
negative_passages.docid: 95206
negative_passages.text: If $\{u,v,w\}$ is a basis for $V$, then $\{u+v+w,v+w,w\}$ is also a basis: is this proof correct?
negative_passages.docid: 132300
negative_passages.text: Dimensions of vector spaces in an exact sequence
negative_passages.docid: 61718
negative_passages.text: Can a basis for a vector space be made up of matrices instead of vectors?
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 116823
negative_passages.text: VERIFYING: Proving an $n \times n$ Matrix Vector Space
negative_passages.docid: 68526
negative_passages.text: Polynomials as vector spaces?
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 59803
negative_passages.text: Converse of Schur's Lemma in finite dimensional vector spaces
negative_passages.docid: 13658
negative_passages.text: Distinction between vectors and points
negative_passages.docid: 17748
negative_passages.text: Is there a quick proof as to why the vector space of $\mathbb{R}$ over $\mathbb{Q}$ is infinite-dimensional?