prove that for an idempotent matrix, trace=rank
65783
Proving: "The trace of an idempotent matrix equals the rank of the matrix"
71631
About idempotent and invertible matrix
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
15197
Relation between trace and rank for projection matrices
97040
Question about an application of the Rank-Nullity theorem
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
90506
Finite multiplicative group of matrices with sum of traces equal to zero.
143608
Show the Trace$(B)^{2} \leq$ nTrace$(B^{T}B)$
11895
If $AB=0$ prove that $\mathrm{rank}(A)+\mathrm{rank}(B)\leq n$
69606
How to prove rank(A+) is no more than rank(A)?
146984
Prove: Full Rank and a solution os linear system
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
27821
A problem on rank of $A$ and $\operatorname{adj}(A)$
73297
Two idempotent matrices are similar iff they have the same rank
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
20241
Find the trace of the matrix?
70528
Rank of a Matrix Sum