An example of no linear map from a vector space to itself that satisfy $T(v+w)=T(v)+T(w)$?
158909
Importance of the homogeneity assumption in definition of linear map
60692
Is this map to a finite dimensional topological vector space an open map?
15300
How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
105014
Is the zero vector in $\mathbb{R}^n$ by itself a subspace of $\mathbb{R}^n$?
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
117986
Are there linear transformations from vector spaces over different fields?
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
47015
Vector Space Structures over ($\mathbb{R}$,+)
126303
Are there linear operators and vector spaces in classical physics?
98696
Is the exponential map ever not injective?
92600
Let $V$ be a $K$-vector space, $f: V \rightarrow V$ a linear map. Under some condition, show that $v, f(v),...,f^n(v)$ are linearly independent.
48990
Linear map $f:V\rightarrow V$ injective $\Longleftrightarrow$ surjective
13880
Example of vector space such that $cv = 0$ where $c \ne 0$ and $v \ne \vec{0}$
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.
24657
Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Comment on S.
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
140212
Prove that there exists a unique linear map that extends the map from a basis