Linear independence of difference of vectors $v_1-v_2,v_2-v_3,v_3-v_4,v_4-v_1$
43871
Is this subset linearly independent or linearly dependent?
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
127285
Inverse images of images, images of inverse images of a set of vectors
72567
Does a set of $n$ independent vectors in $R^{n}$ always span $R^{n}$?
127052
Independence of non-constant real variables
30017
Orthogonality and linear independence
79061
show that {$(x_1,x_2,x_3,x_4)\in\mathbb{F}^4$:$x_3=5x_4+b$} is a subspace
54461
Showing independence of random variables
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
111031
Matrix rank and linear independence of functions
88956
For any three vectors $x,y,z\in\mathbb{R}^d$, we have $ \|y-z\|\cdot\|x\|\leq\|x-y\|\cdot\|z\|+\|z-x\|\cdot\|y\|$
155228
$X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
34272
Proving definition of norms induced by vector norms
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
59598
The vectors are orthonormal
113326
Proving orthogonality of vectors in a complex vector space