Prove that $\{ \sin(x), \sin^2(x), \sin^3(x)\}$ is linearly independent in $F(\Bbb R)$
99105
Are the functions $\sin^n(x)$ linearly independent?
94363
Prove: Any open interval has the same cardinality of $\Bbb R$ (without using trigonometric functions)
31898
Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
16253
Proof that $|\sin(nx)| \le n|\sin(x)|$
66500
Proving that orthogonal vectors are linearly independent
143072
Proving $|\sin x - \sin y| < |x - y|$
8291
If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
130765
Linear dependence of $\left\{x^{n}\,\colon\, n\in\mathbb{N}\right\}$
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
26183
Prob. 9, Sec. 4.3 in Kreyszig's Functional Analysis Book: Proof of the Hahn Banach Theorem without Zorn's Lemma
135641
Algebraic independence of exponentials
20192
Prove that: $(f(x))^{2} + (f'(x))^{2} \leqslant \max(a,b)$ where $(a,b) \in \mathbb{R}^2$
39409
$X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$
822
Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
27072
If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
36878
Prove that $\operatorname{SL}(n,\Bbb R)$ is connected.
62058
How to prove $1$,$\sqrt{2},\sqrt{3}$ and $\sqrt{6}$ are linearly independent over $\mathbb{Q}$?