$A,B$ are two real positive matrices then $\det (A+B) > \max(\det A , \det B)$
102817
$A,B\in M_{n}(\mathbb{R})$ so that $A>0, B>0$, prove that $\det (A+B)>\max (\det(A), \det(B))$
158844
If $a$ and $b$ are positive real numbers such that $a+b=1$, prove that $(a+1/a)^2+(b+1/b)^2\ge 25/2$
73697
Let $A, B$ be $n\times n$ with $n\ge 2$ nonsingular matrices with real entries such that $A^{-1} + B^{-1} =(A+B)^{-1}$
70711
Inequality between 2 norm and 1 norm of a matrix
125348
Does $\det(A + B) = \det(A) + \det(B)$ hold?
46308
Simultaneous diagonlisation of two quadratic forms, one of which is positive definite
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
49330
If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
87262
How to prove positive semidefiniteness of two matrices through Schur Complement?
2109
Max dimension of a subspace of singular $n\times n$ matrices
20309
Product and sum of positive operators is positive
51347
Prove that $|a|\leq \max\{|b|,|c|\}$ if $b\leq a \leq c$
73807
Prove positive definiteness
59396
Show that the rank of $A+B$ is no more than the sum of the ranks of $A$ and $B$
85550
Positive definiteness of difference of inverse matrices
90964
Prove: symmetric positive definite matrix
12868
Is the product of symmetric positive semidefinite matrices positive definite?