If matrices $A,B$ and $(A^2-B^2)$ are all positive semidefinite, is $A-B$ also?
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
147207
Is it always true that $\det(A^2+B^2)\geq0$?
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
33560
Show that matrices $A$ and $B$ commute if and only if $\begin{vmatrix} b & a-c \\ e & d-f\end{vmatrix}=0.$
67820
Showing that $(A_{ij})=\left(\frac1{1+x_i+x_j}\right)$ is positive semidefinite
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
16250
If $B_1,B_2$ and $B_2,B_3$ are MUBs, can we conclude that either $B_1,B_3$ are MUBs, or they have equivalent Hadamard matrices?
36775
Matrix semi-positive definite
90486
If $(A-B)^2=O_2$ then $\det(A^2 - B^2)=(\det(A) - \det(B))^2$
30268
Positive definite matrix must be Hermitian
82097
If $A \succeq B$, is it true that $B^{-1} \succeq A^{-1}$?
51834
Positivity of a determinant
3330
Square matrices, ABA = A?
63920
Does the fact that matrices $A, B$ are similar imply that $A+cI$ is similar to $B+cI$?
147490
If matrix $AB=A$, does it mean B must be an identity matrix?
29454
A and B are real, symmetric and positive semi-definite matrices of the same order; is AB diagonalizable?
75039
Smallest positive element of $ \{ax + by: x,y \in \mathbb{Z}\}$ is $\gcd(a,b)$