Show $X^TX$ is not invertible
14161
Proof of when is $A=X^TX$ invertible?
68724
$||T-I|| < 1$ implies that $T$ is invertible.
85845
Matrix with zeros on diagonal and ones in other places is invertible
18160
How to show that the group of nonzero real numbers under multiplication is not isomorphic to the group of real numbers under addition?
52946
If $X$ is an orthogonal matrix, why does $X^TX = I$?
155136
$x\in \{\{\{x\}\}\}$ or not?
25682
If $A$ is an $m\times n$ matrix, $B$ is an $n\times m$ matrix and $n<m$, then $AB$ is not invertible.
4517
Showing a $2\times2$ matrix is invertible
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
55026
$\mathbb{Q}[X,Y]/(Y^2-X^3)$ is not a UFD
124734
If $A^3=O$ is the matrice $A^2-A+I$ invertible?
126862
Confused about $x \notin x$ example in Axiom of Specification
67058
Prove that $\text{rank}(X^TX)=\text{rank}(X)$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
76297
What is the inverse of the $\mbox{vec}$ operator?
63475
Is there any connection between a matrix being invertible and being diagonalizable?
61484
Continuously invertible operators