If $A\ B$ are symmetric positive definite matrices then $A>B$ iff $\sqrt{A}>\sqrt{B}$
4396
If $A^2\succ B^2$, then necessarily $A\succ B$
75211
Theorem about positive matrices
82410
Find $C$, if $A=CBC$, where $A$,$B$,$C$ are symmetric matrices.
134131
Squared norm of matrix equal to squared norm of its transpose
20921
If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \leq A \leq B$, then det $A \leq$ det $B$.
54211
If $A$ and $B$ are positive definite, then is $B^{-1} - A^{-1}$ positive semidefinite?
42500
Let $A$ and $B$ be matrices over $\mathbb C$. Then pick out the correct statements.
98631
Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$
116309
Is this matrix positive semi-definite?
94424
Matrices and Eigenvalues of Norm
114208
Does non-symmetric positive definite matrix have positive eigenvalues?
46308
Simultaneous diagonlisation of two quadratic forms, one of which is positive definite
120867
How prove this two symmetric matrices $AB=0$
2798
A and B are nxn matrices, $A =B^TB$. Prove that if rank(B)=n, A is pos def, and if rank(B)<b, A is pos semi-def.
41813
How to prove positive (semi-)definitness in matrix notation without numbers
23264
Inequality $ \vert \sqrt{a}-\sqrt{b} \vert \leq \sqrt{ \vert a -b \vert } $
19649
A question about the proof of "a symmetric matrix has real eigenvalues".