Prove linear functionals
53528
If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
18921
Linear Transformations: Proving 1 dimensional subspace goes to 1 dimensional
45676
Showing that $f$ is linear function if $\forall z \in \mathbb{C}$, $|f(z)| \leq 1 + |z|$.
140212
Prove that there exists a unique linear map that extends the map from a basis
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
149739
Prove: $f(t)\leq t+1$
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
19078
Prove an interpolation inequality
92202
Linear separability for a sum of kernel functions
83461
Continuous iff composition with every linear functional is continuous
62887
Proof that a linear transformation is continuous
41520
Prove that $L(V,W)$ forms a vector space
3820
Prove that $||x|-|y||\le |x-y|$
84448
Any positive linear functional $\phi$ on $\ell^\infty$ is a bounded linear operator and has $\|\phi \| = \phi((1,1,...)) $
102529
Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
126256
Prove limit of function
94077
Proof of linear independence of $e^{at}$