Is it Rank$(A^{T}A)$= Rank$(AA^{T})$?
6905
Rank of product of a matrix and its transpose
65628
what happens to rank of matrices when singular matrix multiply by non-singular matrix??
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
126747
Null space for $AA^{T}$ is the same as Null space for $A^{T}$
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
69606
How to prove rank(A+) is no more than rank(A)?
119435
Rank of the difference of matrices
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
30923
Is the matrix $A^*A$ and $AA^*$ hermitian?
118212
Is it true that $A^A\simeq P(A)$?
3150
Is there an intuitive interpretation of $A^TA$ for a data matrix $A$?
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
103061
Why is it true that $\mathrm{adj}(A)A = \det(A) \cdot I$?
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
116389
If $\exp(t(A + B)) = \exp(tA) \exp(tB)$ for all $t \geq 0$ then $A,B$ commute
44383
Finding rank of a matrix depending on parameter a