An mm-order nn-dimensional square real tensor AA is a multidimensional
array of nmnm elements of the form
{A=(Ai1…im)A=(Ai1…im), Ai1…im RAi1…im R, 1≤i1, ∈ ∈
…,im≤n.1≤i1,…,im≤n.}
(A square matrix of order nn is a 22-order nn-dimensional square tensor).
An mm-order nn-dimensional square real tensor is said to be a nonnegative
(positive) tensor if all its entries are nonnegative (positive). We shall
discuss the Perron-Frobenius theory for nonnegative tensors. Using these
results we establish a sufficient condition for the positive semidefiniteness
of homogenous multivariable polynomials.
