Prove that $X'X$ is rank-preserving of X
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
101712
Let $X$ be obtained by removing finitely many lines from $\mathbb{R}^3$. How do I prove $X$ is connected?
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
121264
Prove that rank $(g \circ f)\le \min[\operatorname{rank}(f),\operatorname{rank}(g)]$; $g$ and $f$ are linear mappings
41436
rank of complex conjugate transpose matrix property proof
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
83291
Prove that $p(x)=(x-a)q(x)$ for some $q(x)\in R[x]$ of degree= (degree of $p)-1$.
70304
Prove there are $\xi$, $\eta$ with $f'(\xi)f'(\eta)=1$
47810
$C(X)$ is separable when $X$ is compact?
46265
Minimal polynomial of the operator $T:V\oplus W\to V\oplus W$
104097
An idempotent operator is compact if and only if it is of finite rank
14161
Proof of when is $A=X^TX$ invertible?
74792
$(X,\tau)$ needs to be $T_1$ in order to guarantee that $A'$ is closed?
94383
Prove that $A^TD-C^TB=I$
69606
How to prove rank(A+) is no more than rank(A)?
123483
Prove that $\operatorname{rank}(A) + \operatorname{rank}(B) \ge \operatorname{rank}(A + B)$