If $\Vert Tx-Ty \Vert = \Vert x-y \Vert$ for all $x,y \in X$ and $T(0)=0$ then T is a linear aplication.
71975
Showing that an Isometry on the Euclidean Plane fixing the origin is Linear
138343
How to prove that the set $\{\sin(x),\sin(2x),...,\sin(mx)\}$ is linearly independent?
71203
Proving that two systems of linear equations are equivalent if they have the same solutions
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
3433
Proof if $a \vec v = 0$ then $a = 0$ or $\vec v = 0$
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
75855
Show that $\det{(A + sxy^*)}$ is linear in $s$
114458
$f$ is entire and maps a rectangle to a rectangle, then $f$ is linear
54217
Let $V$ be a vector space. Determine all linear transformations $T:V \rightarrow V$ such that $T=T^2$.
31898
Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent
92774
Prove that a linear subspace of $C([0,1])$ is closed
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
112284
If $\mid a_{jj}\mid \gt \sum_{i \neq j} \mid a_{ij} \mid$ then vectors $a_1,\dots ,a_n \in \mathbb{R}^n$ are linearly indendent.
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
72920
$x \perp y$ if and only if $\Vert x + \alpha y \Vert \ge \Vert x \Vert$ for all scalars $\alpha$
5373
Additive function $T: \mathbb{R} \rightarrow \mathbb{R}$ that is not linear.
2315
How to prove that $\lVert x + y\rVert = \lVert x\rVert + \lVert y \rVert \implies \lVert tx + (1-t)y\rVert = t\lVert x\rVert + (1-t)\lVert y \rVert$?