Is $\text{rank} (AA^*)=\text{rank}(A)$ for all nonsquare matrices?
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
60598
Matrix $A^T A$ as sum of outer products
41026
How to prove and interpret $\operatorname{rank}(AB) \leq \operatorname{min}(\operatorname{rank}(A), \operatorname{rank}(B))$?
149219
If $A$ is a non-square matrix with orthonormal columns, what is $A^+$?
57296
A non-diagonal $4\times4$ matrix such that $A^3=A^2=0$ and its rank is $2$
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
62283
How can I quickly know the rank of this / any other matrix?
122853
Show that $\operatorname{rank}(A) = \operatorname{rank}(B)$
60736
Looking for an intuitive explanation why the row rank is equal to the column rank for a matrix
65628
what happens to rank of matrices when singular matrix multiply by non-singular matrix??
65062
Prove $\text{rank}(A) \geq \frac{(\text{tr}(A))^2}{\text{tr}(A^2)}$ when $A$ is Hermitian
64517
Prove that row rank of a matrix equals column rank
34372
Are $10\times 10$ matrices spanned by powers of a single matrix?
94424
Matrices and Eigenvalues of Norm
34536
Columns of matrix $A_{m \times n}$ span $\mathbb{R}^{m}$
147014
Matrix algebra: If $A^2=0$, Proof rank(A) $\le \frac{n}{2}$
70157
Is every matrix $A$ such that $A^k=I$ diagonalizable?