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Seminar

Date/Time: 
Tuesday, March 15, 2016 -
03:30 to 04:30
Venue: 
M5
Speaker: 
Rajesh Kannan
Affiliation: 
Univeristy of Manitoba
Title: 
Nonnegative tensors and their applications

An $m$-order $n$-dimensional square real tensor $\mathcal{A}$ is a multidimensional array of $n^m$ elements of the form$\mathcal{A} = (A_{i_1\dots i_m})$, $A_{i_1\dots i_m} \in \mathbb{R}$, $1 \leq i_1, \dots , i_m \leq n.$ (A square matrix of order $n$ is a $2$-order $n$-dimensional square tensor.) An $m$-order $n$-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.

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