query: Linear independence between vectors and subvector spaces
positive_passages.docid: 146664
positive_passages.text: The union of two linearly independent subsets
negative_passages.docid: 74465
negative_passages.text: One-dimensional vector space and it's subspaces
negative_passages.docid: 111031
negative_passages.text: Matrix rank and linear independence of functions
negative_passages.docid: 122305
negative_passages.text: Proof of matrix norm property: submultiplicativity
negative_passages.docid: 144557
negative_passages.text: Linearly independent functionals
negative_passages.docid: 116823
negative_passages.text: VERIFYING: Proving an $n \times n$ Matrix Vector Space
negative_passages.docid: 92202
negative_passages.text: Linear separability for a sum of kernel functions
negative_passages.docid: 44710
negative_passages.text: Vector space of real vectors over field complex scalars.
negative_passages.docid: 132492
negative_passages.text: If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
negative_passages.docid: 59647
negative_passages.text: Vector spaces with fractional dimension
negative_passages.docid: 122623
negative_passages.text: Geometric intuition for the tensor product of vector spaces
negative_passages.docid: 133711
negative_passages.text: Orthogonal basis for infinite-dimensional vector spaces
negative_passages.docid: 145294
negative_passages.text: Independence of linear combination of multivariate distribution
negative_passages.docid: 81229
negative_passages.text: Show that $(C([a,b]),\|{\cdot}\|_2)$ is not a complete normed vector space
negative_passages.docid: 30720
negative_passages.text: If the dot product between two vectors is $0$, are the two linearly independent?
negative_passages.docid: 43282
negative_passages.text: Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
negative_passages.docid: 137873
negative_passages.text: Problems that involves two facts in the definition of vector spaces