query: Can we deduce that any additive map from V to W, over the field $R$ is actually a linear transformation?
positive_passages.docid: 13086
positive_passages.text: Overview of basic facts about Cauchy functional equation
negative_passages.docid: 76586
negative_passages.text: How to prove that linear transformations transforms lines into lines
negative_passages.docid: 24004
negative_passages.text: General form of a linear transformation
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: 5644
negative_passages.text: Is a right inverse of a surjective linear map linear?
negative_passages.docid: 21578
negative_passages.text: Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
negative_passages.docid: 98696
negative_passages.text: Is the exponential map ever not injective?
negative_passages.docid: 94378
negative_passages.text: Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
negative_passages.docid: 127488
negative_passages.text: If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
negative_passages.docid: 125435
negative_passages.text: Practical application for linear transformations
negative_passages.docid: 88728
negative_passages.text: Dimensions of vector subspaces in a direct sum are additive
negative_passages.docid: 71037
negative_passages.text: Is exponential map locally a diffeomorphism w.r.t. base point?
negative_passages.docid: 63845
negative_passages.text: Diffeomorphism $f:U\to V$ then $Df:\mathbb{R^n}\to\mathbb{R^m}$ will be linear isomorphism hence $n=m$
negative_passages.docid: 34670
negative_passages.text: What exactly is the fixed field of the map $t\mapsto t+1$ in $k(t)$?
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 86034
negative_passages.text: Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?
negative_passages.docid: 93776
negative_passages.text: Bijective mapping between $\mathbb{R}^2$ and $\mathbb{R}$?