query: Prove that if $T: V \rightarrow W$ is an application s.t $T(x+y)=T(x)+T(y)$, then T is a linear transformation
positive_passages.docid: 5373
positive_passages.text: Additive function $T: \mathbb{R} \rightarrow \mathbb{R}$ that is not linear.
negative_passages.docid: 37813
negative_passages.text: If $T\colon \mathbb R^n \to \mathbb R^n $ linear and $T^2 = kT$
negative_passages.docid: 48990
negative_passages.text: Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
negative_passages.docid: 45416
negative_passages.text: linear transformation $T$ is onto if and only if $T^*$ is one to one
negative_passages.docid: 63705
negative_passages.text: Show that rodriques formula is a linear transformation?
negative_passages.docid: 44453
negative_passages.text: Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)
negative_passages.docid: 73406
negative_passages.text: Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
negative_passages.docid: 131998
negative_passages.text: let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
negative_passages.docid: 152887
negative_passages.text: 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.
negative_passages.docid: 53971
negative_passages.text: If $g:V \rightarrow V$ is an injective linear transformation. Prove if $V$ is finite dimensional then $g$ is surjective.
negative_passages.docid: 99300
negative_passages.text: Prove if $W \subset V$ is a subspace such that $T(W)\subset W$, then $V/W$ is finite-dimensional.
negative_passages.docid: 131480
negative_passages.text: Proof that composition of invertible linear transformations is invertible (without determinants)
negative_passages.docid: 51209
negative_passages.text: A linear transformation satisfying $P^2 = P$
negative_passages.docid: 133087
negative_passages.text: Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
negative_passages.docid: 128229
negative_passages.text: Proving that the transformation obtained from an adjoint pair is natural
negative_passages.docid: 20879
negative_passages.text: Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?
negative_passages.docid: 145104
negative_passages.text: $T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$