If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
57070
Dimensionality of null space when Trace is Zero
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
116908
Basis for set of nxn matrices with trace = 0
131998
let ${v_1}, {v_2} $ be orthonormal basis for subspace $W$. Prove that if $z$ is a vector in $W$, then
31606
Do matrices $ AB $ and $ BA $ have the same minimal and characteristic polynomials?
151332
If $A,B$ have eigenvalues $\pm1$, what can I say about the eigenvalues of $AB,BA$?
133482
$AB-BA$ is a nilpotent matrix if it commutes with $A$
113261
How to find a vector space V and decompositions $V=A\oplus B = C\oplus D$ with $A$ isomorphic to $C$ but $B$ is not isomorphic to $D?$
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
124786
Prove that V contains a subspace of each dimension
30037
What information does the trace of a matrix give?
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
73286
Show that the set of all symmetric, real matrices is a subspace, determine the dimension
74460
Matrices A+B=AB implies A commutes with B
106986
Eigenvalues of $AB$ and $BA$
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
122951
If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?