Necessary Condition for linear independence of functions
111031
Matrix rank and linear independence of functions
49896
A criterion for independence based on Characteristic function
39409
$X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$
48679
measurability of supremum of a class of functions
145039
Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
144557
Linearly independent functionals
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
994
Linear independence of vectors that form non-square matrix
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
83461
Continuous iff composition with every linear functional is continuous
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
93910
Equality in Cauchy-Schwarz Inequality implies linear dependence.
107248
Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
54957
The necessary and sufficient condition for a unit element in Euclidean Domain
131000
A proof of a criterion of vanishing of a function.