All Questions

Consider two symmetric and real matrices $A,B\in\mathbb{R}^n$ and definie $A+iB$. Note that $A+iB$ is not hermitian in this case. There are many results based on Brendixson and Courant-Fischer, saying,...

Suppose that $A$ is a $n\times n$ positive matrix, whose eigenvalues are $a_1\ge a_2\ldots \ge a_n>0;$ $B$ is a $m \times m$ positive matrix, whose eigenvalues are $b_1\ge b_2\ldots \ge b_m>0;$ ...

I am reading a paper on covariance matrix estimation, and in this paper is introduced a class of covariance matrices: \begin{equation} U(q, c_0(p),M)=\{\Sigma: \sigma_{ii}\leq M,\quad \max_j\sum_{j=1}^...