Does there exist an infinite $S \subset \Bbb R^3$ such that any three vectors in $S$ are linearly independent?
58774
There exist an infinite subset $S\subseteq\mathbb{R}^3$ such that any three vectors in $S$ are linearly independent.
90826
Constructing a subset not in $\mathcal{B}(\mathbb{R})$ explicitly
146243
Does there exist a matrix $\mathbf{A}\in\mathbb{R}^{3\times3}$ such that $\mathbf{A}^{2}=-\mathbf{I}$?
132492
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
60684
Determine whether the set $W$ is a subspace in $\mathbb{R}^{3}$
96354
Linear independence of $\sin(x)$, $\sin(2x)$, $\sin(3x)$ in Map($\mathbb{R},\mathbb{R}$)
91087
For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
115954
how to find maximal linearly independent subsets
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
76498
Does every linearly independent set of n vectors in $R^n$ forms a basis in $R^n$?
42495
Determine if the following sets of vectors are linearly independent
117211
Infinite linear independent family in a finitely generated $A$-module
126769
Linear independence of columns implies non-zero determinant
66500
Proving that orthogonal vectors are linearly independent
723
Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$?
75104
Existence of some type matrix
64395
If $v_1,...,v_r$ are eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.