If $MM^{'}$ is positive definite, $M$ is invertible?
36567
$A^{T}A$ positive definite then A is invertible?
79276
Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$
106398
If $A$ is invertible show that $\det(A) \neq 0$
104413
Is the exponential of $-d$ a positive definite kernel for a general metric space $(X, d)$?
146487
Can a non-square matrix be called "invertible"?
5475
Derivative of the inverse of a matrix
73406
Prove that $E_{\lambda}(T)=E_{\lambda^{-1}}(T^{-1})$ if $T$ is an invertible linear operator on a finite dimensional vector space $V$
54211
If $A$ and $B$ are positive definite, then is $B^{-1} - A^{-1}$ positive semidefinite?
119301
Is the following matrix invertible?
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
131480
Proof that composition of invertible linear transformations is invertible (without determinants)
15175
When does a Möbius transformation map $\Im(z)>0$ to itself?
69349
If $A$ is positive definite, then $\int_{\mathbb{R}^n}\mathrm{e}^{-\langle Ax,x\rangle}\text{d}x=\left|\det\left({\pi}^{-1}A\right)\right|^{-1/2}$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
78307
Under what conditions is $AA^T$ invertible?
75215
Properties of invertible matrices