$f\circ f$ is linear implies $f$ is linear
124139
If $f(f(x))$ is a linear function, must $f(x)$ be linear?
91352
If $\Re(f)$ is bounded then f is constant.
78344
Nonconstant linear functional on a topological vector space is an open mapping
105700
Proving $\,f$ is constant.
127488
If $L:\mathbb{R}^n \rightarrow \mathbb{R}^m$ and $m<n$ linear trans. What does this tell about injectivity and surjectivity?
91911
A linear operator between $C[0,1]$ and $C[0,1]$ defined as $Tf = f + \int f$; Show $T$ is an isomorphism
77891
$(U\circ T)^{*} = T^{*}\circ U^{*}$
92534
Prove that any finite subset of a linearly independent set is linearly independent
75266
$f(a+b)=f(a)+f(b)$ but $f$ is not linear
70912
If $g\circ f$ is injective and $f$ is surjective then $g$ is 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.
6291
Proving something is a linearly independent subset
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
11798
If $f \circ g$ is onto then $f$ is onto and if $f \circ g$ is one-to-one then $g$ is one-to-one
72006
Suppose $f(x)$ is linear i.e. $f(x + y) = f(x) +f(y) $ and monotone on $[-\infty, +\infty]$, then $f(x) = ax$, a real.
126808
Is it true that if $f(x)$ has a linear factor over $\mathbb{F}_p$ for every prime $p$, then $f(x)$ is reducible over $\mathbb{Q}$?
93121
How to prove there exists a linear transformation?