Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation estimation for the parallel sum of Hermitian positive
  semi-definite matrices   Let $\mathbb{C}^{n\times n}$ be the set of all $n \times n$ complex matrices.
For any Hermitian positive semi-definite matrices $A$ and $B$ in
$\mathbb{C}^{n\times n}$, their new common upper bound less than $A+B-A:B$ is
constructed, where $(A+B)^\dag$ denotes the Moore-Penrose inverse of $A+B$, and
$A:B=A(A+B)^\dag B$ is the parallel sum of $A$ and $B$. A factorization formula
for $(A+X):(B+Y)-A:B-X:Y$ is derived, where $X,Y\in\mathbb{C}^{n\times n}$ are
any Hermitian positive semi-definite perturbations of $A$ and $B$,
respectively. Based on the derived factorization formula and the constructed
common upper bound of $X$ and $Y$, some new and sharp norm upper bounds of
$(A+X):(B+Y)-A:B$ are provided. Numerical examples are also provided to
illustrate the sharpness of the obtained norm upper bounds.

11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph