A Linear map A whose trace is 0.
52928
If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$
140212
Prove that there exists a unique linear map that extends the map from a basis
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.
44361
An automorphism that has no fixed points except for the identity and is its own inverse implies commutativity
93121
How to prove there exists a linear transformation?
121264
Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
96530
Matrix representation of linear map in this basis
103924
Kernel of a substitution map
33129
A linear map $S:Y^*\to X^*$ is weak$^*$ continuous if and only if $S=T^*$ for som $T\in B(X,Y)$
48419
Difference between $\mathbb{R}$-linear and $\mathbb{C}$-linear maps
93606
Showing that $C[0,1]$ is not complete
157269
If $\alpha_{1},\ldots,\alpha_{m}$ are vectors different from zero vector, then there is a linear functional $f$ such that $f(\alpha_{i})\neq 0$
5644
Is a right inverse of a surjective linear map linear?
101319
Properties of a continuous map $f : \mathbb{R}^2\rightarrow \mathbb{R}$ with only finitely many zeroes
93923
No surjective bounded linear map from $\ell^2(\mathbf{N})$ to $\ell^1(\mathbf{N})$
158343
how to prove an element is non-zero in a tensor-product
29583
Characterization of the trace function