Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator inequalities and gyrolines of the weighted geometric means   We consider in this paper two different types of the weighted geometric means
of positive definite operators. We show the component-wise bijection of these
geometric means and give a geometric property of the spectral geometric mean as
a metric midpoint. Moreover, several interesting inequalities related with the
geometric means of positive definite operators will be shown. We also see the
meaning of weighted geometric means in the gyrogroup structure with finite
dimension and find the formulas of weighted geometric means of 2-by-2 positive
definite matrices and density matrices.

23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc