Prove that if $A$ is invertible then $AA^\top$ is positive definite
36567
$A^{T}A$ positive definite then A is invertible?
20309
Product and sum of positive operators is positive
20110
How to prove $(AB)^T=B^T A^T$
145397
How to prove that for every $i$, $a_i = i$
52791
Invertibility of an operator $T$ if $\|I-T\|<1$
68724
$||T-I|| < 1$ implies that $T$ is invertible.
135252
If $M$ is positive definite, then $\operatorname{det}{(M)}\leq \prod_i m_{ii}$
35345
How do i prove invertibility of this linear transformation
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
81775
Prove $a^\alpha b^{1-\alpha} \le \alpha a + (1 - \alpha)b, \; a,b > 0,\; 0 < \alpha < 1$
42809
How can we show that $(I-A)$ is invertible?
74341
Proving an invertible matrix which is its own inverse has determinant $1$ or $-1$
99600
Show that a 2x2 matrix A is symmetric positive definite if and only if A is symmetric, trace(A) > 0 and det(A) > 0
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
106398
If $A$ is invertible show that $\det(A) \neq 0$
38266
How to prove that exponential kernel is positive definite?
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?