How to prove $rank(A^+)$ is no more than rank(A)?
69606
How to prove rank(A+) is no more than rank(A)?
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
41813
How to prove positive (semi-)definitness in matrix notation without numbers
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
118039
How prove $p!|(a+1)$ if $p!|a^p+1$
33903
Prove that $(1+a_1) \cdot (1+a_2) \cdot \dots \cdot (1+a_n) \geq 2^n$
155451
Upper bound for the rank of a nilpotent matrix , if $A^2 \ne 0$
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
55018
Prove that $A^*A + I$ is invertible
97487
How to prove whether a matrix has rank $1$
74611
$\operatorname{Adj} (\mathbf I_n x-\mathbf A)$ when $\operatorname{rank}(\mathbf A)\le n-2$
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
48660
Proof that determinant rank equals row/column rank
35897
Proof of: $AB=0 \Rightarrow Rank(A)+Rank(B) \leq n$
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$