query: Do any n linearly independent vectors span $R^n$? If yes, what's the proof?
positive_passages.docid: 72567
positive_passages.text: Does a set of $n$ independent vectors in $R^{n}$ always span $R^{n}$?
negative_passages.docid: 63036
negative_passages.text: Proving that $\dim(\mathrm{span}({I_n,A,A^2,...})) \leq n$
negative_passages.docid: 60063
negative_passages.text: Independence between random vectors
negative_passages.docid: 94077
negative_passages.text: Proof of linear independence of $e^{at}$
negative_passages.docid: 105014
negative_passages.text: Is the zero vector in $\mathbb{R}^n$ by itself a subspace of $\mathbb{R}^n$?
negative_passages.docid: 152147
negative_passages.text: Why is a set of orthonormal vectors linearly independent?
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 40409
negative_passages.text: If a subspace S is spanned by $n$ vectors, any subset of S with $m>n$ vectors is linearly dependent
negative_passages.docid: 91087
negative_passages.text: For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
negative_passages.docid: 146143
negative_passages.text: Question about proof that finite-dimensional subspaces of normed vector spaces are direct summands
negative_passages.docid: 141799
negative_passages.text: Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
negative_passages.docid: 138343
negative_passages.text: How to prove that the set $\{\sin(x),\sin(2x),...,\sin(mx)\}$ is linearly independent?
negative_passages.docid: 17087
negative_passages.text: Question concerning linear combinations of vectors and linear independence in Linear Algebra.
negative_passages.docid: 119782
negative_passages.text: Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
negative_passages.docid: 128093
negative_passages.text: Regarding the values that n and r can take in $\binom{n}{r}$
negative_passages.docid: 34536
negative_passages.text: Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
negative_passages.docid: 109228
negative_passages.text: Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent