Endomorphism rank: prove that $r_k-r_{k+1} \geq r_{k+1}-r_{k+2}$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
9562
Proving that surjective endomorphisms of Noetherian modules are isomorphisms and a semi-simple and noetherian module is artinian.
41398
For a ring $R$, does $\operatorname{End}_R(R)\cong R^{\mathrm{op}}$?
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
97487
How to prove whether a matrix has rank $1$
154142
Finding a specific basis for an endomorphism
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
75117
$\mathrm{rank}(AB-BA)=1$ implies $A$ and $B$ are simultaneously triangularisable
97608
Showing a Ring of endomorphisms is isomorphic to a Ring
23037
Computing the order of $\mathrm{SL}_2(\mathbb F_p)$ as the kernel of $\mathrm{GL}_2(\mathbb F_p)$
95513
Proving $W$ is a subspace of $P_{2}$
25260
Extension of a morphism $k^*\rightarrow X$ to $\mathbb{P}^1\rightarrow \overline{X}$
127886
Artin's lemma and some morphisms.
41436
rank of complex conjugate transpose matrix property proof
23224
$\mbox{rank}(A)=1$ implies $\det(A+I)=\mbox{trace}(A)+1$