Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Square roots of H-nonnegative matrices   Roots of matrices are well-studied. The conditions for their existence are
understood: The block sizes of nilpotent Jordan blocks, arranged in pairs, have
to satisfy some simple algebraic property.
  More interesting are structured roots of structured matrices. Probably the
best known example is the existence and uniqueness of positive definite square
roots of a positive definite matrix. If one drops the requirement of positive
definiteness of the square root, it turns out that there exists an abundance of
square roots. Here a description of all canonical forms of all square roots is
possible and is straight forward.
  H-nonnegative matrices are H-selfadjoint and are nonnegative with respect to
an indefinite inner product with Gramian H. An H-nonnegative matrix $B$ allows
a decomposition in a negative definite, a nilpotent H-nonnegative, and a
positive definite matrix, B=B_- \oplus B_0 \oplus B_+. The interesting part is
B_0, as only Jordan blocks of size one and two occur. Determining a square root
of B reduces to determining a square root of each of B_-, B_0, and B_+. Here we
investigate for an H-nonnegative matrix: its square roots without additional
structure, as well as its structured square roots that are H-nonnegative or
H-selfadjoint.
  For these three classes of square roots of H-nonnegative matrices we show a
simple criterion for their existence and describe all possible canonical forms.
This is based mainly on known results but an important new part is that in all
three cases we describe all possible square roots of the nilpotent
H-nonnegative matrix B_0 explicitly. Moreover, we show how our results can be
applied to the conditional and unconditional stability of H-nonnegative square
roots of H-nonnegative matrices, where the explicit description of the square
roots of B_0 is used.

30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: eess