query: How many bases can be formed given a set of vectors?
positive_passages.docid: 148454
positive_passages.text: how many linearly independed vectors combinations may I extract from a set of vectors
negative_passages.docid: 27478
negative_passages.text: Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
negative_passages.docid: 17087
negative_passages.text: Question concerning linear combinations of vectors and linear independence in Linear Algebra.
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
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: 134999
negative_passages.text: Writing empty set as union of basis elements for a topology.
negative_passages.docid: 146098
negative_passages.text: Number of nonempty subsets of a set with $n$ elements
negative_passages.docid: 6432
negative_passages.text: How many ways can N elements be partitioned into subsets of size K?
negative_passages.docid: 4319
negative_passages.text: Vector space can be written as direct sum of subspaces
negative_passages.docid: 85650
negative_passages.text: Number or regions formed when $n$ points on a circle are joined
negative_passages.docid: 37119
negative_passages.text: Determine Which of the following Sets is a Vector Space
negative_passages.docid: 94601
negative_passages.text: Mathematical Induction Question About A Basis Step
negative_passages.docid: 94735
negative_passages.text: Base and Spans, linear space
negative_passages.docid: 97574
negative_passages.text: Jordan form, number of blocks.
negative_passages.docid: 120344
negative_passages.text: Are there nontrivial vector spaces with finitely many elements?
negative_passages.docid: 52888
negative_passages.text: Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$
negative_passages.docid: 39957
negative_passages.text: Product of binomial coefficient as a basis