$\operatorname{rank}(A)=n$ then $\left\lVert{A(A^TA)^{-1}A^T}\right\rVert_2 = 1$
46435
2-norm of the orthogonal projection
45469
If $a_k = \operatorname{rank}(S^k)$, deduce that $a_k - a_{k+1} \geq a_{k+1} - a_{k+2}$
19203
Is the rank of a matrix the same of its transpose? If yes, how can I prove it?
55820
If $A$ is an $n \times n$ matrix and $ A^2 = 0$, then $\text{rank}(A)\le n/2$.
135422
$\operatorname{Hom}(-,A) \cong \operatorname{Hom}(-,A') \Rightarrow A \cong A'$, proof verification
43000
Show $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A+B)$
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
147627
Relation between condition numbers $\kappa(A^T A)$ and $\kappa(A)$
131701
Why is $A^TA$ invertible if $A$ has independent columns?
78575
If $A^2 = I$, then $\operatorname{rank} (A+I) + \operatorname{rank} (A-I) =n$
36567
$A^{T}A$ positive definite then A is invertible?
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
2798
A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
95677
Linear Matrix Inequality of a matrix $T$ with $\| T \|_2 < \rho$
129732
What is $\operatorname{Aut}(\mathbb{Z}_2\oplus \mathbb{Z}_2)$?