If $A \in M_{n \times m}(\mathbb{R})$, why is $\operatorname{rk}(A) = \operatorname{rk}(AA^t)$?
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
147659
Counterexample to "if $f:A\to A$ induces the identity $\hat f:\operatorname{Spec}(A)\to\operatorname{Spec}(A)$, then $f=\operatorname{id}_A$"
30923
Is the matrix $A^*A$ and $AA^*$ hermitian?
15793
Is the formula $(\text{ker }A)^\perp=\text{im }A^T$ necessarily true?
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
127198
What is $\mathbb{C}^{Aut(\mathbb{C}/\mathbb{Q})}$?
79276
Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
75059
Let $T:\mathbb{R}^n\to \mathbb{R}^n$ be a linear transformation...
34714
What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?
111348
Show that $\mathrm{S}_{m} \times \mathbb{N}^{m} \rightarrow \mathbb{N}^{m}$ defines an action of $\mathrm{S}_{m}$ on $\mathbb{N}^{m}$
146847
Given a square matrix A of order n, prove $\operatorname{rank}(A^n) = \operatorname{rank}(A^{n+1})$
128673
Given $A : \mathcal{C} \rightarrow \mathcal{E}$, when does $\operatorname{colim} A = A(1)$?
103427
When is $\operatorname{Hom}_A(M,N)$ finitely generated?
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
106584
If $A^{2n}=I$, then $A^n=\pm I$ where $A\in M_n(\mathbb{R})$