How do I prove that the 2 ranks are equivalent
4952
Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$).
151443
Find two $2 \times 2$ matrices $A$ and $B$ with the same rank, determinant,...but they are not similar.
18018
Proving that $4 \mid m - n$ is an equivalence relation on $\mathbb{Z}$
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
79686
How can I prove these statements?
139743
Necessary condition for have same rank
69043
The equivalence relation generated by a relation
113065
Proving equivalences of statements equivalent to AC
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
60140
Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
76335
Proving that two matrices are congruent, in order to establish a rank and signature result.
48660
Proof that determinant rank equals row/column rank
115663
Proving an isomorphism using the isomorphism theorems
121157
Proof verification: column rank = row rank
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
21758
Rank of the $n \times n$ matrix with ones on the main diagonal and $a$ off the main diagonal