Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Norm Compression Inequality for Block Partitioned Positive
  Semidefinite Matrices   Let $A$ be a positive semidefinite matrix, block partitioned as $$
A=\twomat{B}{C}{C^*}{D}, $$ where $B$ and $D$ are square blocks. We prove the
following inequalities for the Schatten $q$-norm $||.||_q$, which are sharp
when the blocks are of size at least $2\times2$: $$ ||A||_q^q \le (2^q-2)
||C||_q^q + ||B||_q^q+||D||_q^q, \quad 1\le q\le 2, $$ and $$ ||A||_q^q \ge
(2^q-2) ||C||_q^q + ||B||_q^q+||D||_q^q, \quad 2\le q. $$ These bounds can be
extended to symmetric partitionings into larger numbers of blocks, at the
expense of no longer being sharp: $$ ||A||_q^q \le \sum_{i} ||A_{ii}||_q^q +
(2^q-2) \sum_{i<j} ||A_{ij}||_q^q, \quad 1\le q\le 2, $$ and $$ ||A||_q^q \ge
\sum_{i} ||A_{ii}||_q^q + (2^q-2) \sum_{i<j} ||A_{ij}||_q^q, \quad 2\le q. $$

7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat