How to show $\text{rank}(p)=\text{trace}(p)$ for every projector $p$ defined on $\mathbb{R}^n$?
15197
Relation between trace and rank for projection matrices
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
131680
Writing projection in terms of projection matrix
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
147888
Show that $M=\bigcap_{\mathfrak{p}\in\operatorname{Spec}(R)}M_\mathfrak{p}=\bigcap_{\mathfrak{m}\in\text{Max}(R)}M_\mathfrak{m}$ for certain $M$.
79591
Exact Sequences of Modules and Rank
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
77192
How to prove $\text{Rank}(AB)\leq \min(\text{Rank}(A), \text{Rank}(B))$?
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
2907
How do I show that $x$ is a root of $p(x)$ in $F[x]/\langle p(x)\rangle$?
52642
Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
143869
Showing that the norm of the canonical projection $X\to X/M$ is $1$
121221
Rank-Nullity Theorem
69606
How to prove rank(A+) is no more than rank(A)?
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
121264
Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings