Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: P-Tensors, P$_0$-Tensors, and Tensor Complementarity Problem   The concepts of P- and P$_0$-matrices are generalized to P- and P$_0$-tensors
of even and odd orders via homogeneous formulae. Analog to the matrix case, our
P-tensor definition encompasses many important classes of tensors such as the
positive definite tensors, the nonsingular M-tensors, the nonsingular H-tensors
with positive diagonal entries, the strictly diagonally dominant tensors with
positive diagonal entries, etc. As even-order symmetric PSD tensors are exactly
even-order symmetric P$_0$-tensors, our definition of P$_0$-tensors, to some
extent, can be regarded as an extension of PSD tensors for the odd-order case.
Along with the basic properties of P- and P$_0$-tensors, the relationship among
P$_0$-tensors and other extensions of PSD tensors are then discussed for
comparison. Many structured tensors are also shown to be P- and P$_0$-tensors.
As a theoretical application, the P-tensor complementarity problem is discussed
and shown to possess a nonempty and compact solution set.

23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat