Show that the matrix $\big(\frac{1}{a_i + a_j}\big)_{n\times n}$ is positive semidefinite
98631
Postive-semidefiniteness of matrix with entries $1/(a_i+a_j)$
32103
Show that for a $2\times 2$ matrix $A^2=0$
118283
Show that if $A^{n}=I$ then $A$ is diagonalizable.
70606
Show that the LU decomposition of matrices of the form $\left[\begin{smallmatrix}0& x\\0 & y\end{smallmatrix}\right]$ is not unique
34697
Why is the Fisher Information matrix positive semidefinite?
110271
Given a matrix with non-negative real entries, can you algebraically prove that it has a non-negative eigenvalue?
68132
Small positive eigenvalues found for a negative definite matrix
149287
Prove that $A,B>0$ and $A_{ij}0$
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
130066
If $\ \sum_{k=1}^n m(E_n) > n-1,$ then prove that $\bigcap_{k=1}^n E_k$ has positive measure.
86940
Proving an inequality in Eigenvalues of a matrix
128990
Prove that, at least one of the matrices $A+B$ and $A-B$ has to be singular
135171
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
3408
Do positive semidefinite matrices have to be symmetric?
18119
Show that if a,b,c,d are positive then $\frac{ab}{a+b}+\frac{cd}{c+d}\le \frac{(a+c)(b+d)}{a+b+c+d}$
122305
Proof of matrix norm property: submultiplicativity
108589
The inverse of the matrix $\{1/(i+j-1)\}$