Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inequalities and limits of weighted spectral geometric mean   We establish some new properties of spectral geometric mean. In particular,
we prove a log majorization relation between $\left(B^{ts/2}A^{(1-t)s}B^{ts/2}
\right)^{1/s}$ and the $t$-spectral mean $A\natural_t B :=(A^{-1}\sharp
B)^{t}A(A^{-1}\sharp B)^{t}$ of two positive semidefinite matrices $A$ and $B$,
where $A\sharp B$ is the geometric mean, and the $t$-spectral mean is the
dominant one. The limit involving $t$-spectral mean is also studied. We then
extend all the results in the context of symmetric spaces of negative
curvature.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org