##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Harm Derksen

#### University of Michigan, Ann Arbor

## Tensor Decompositions

##### Abstract:

A tensor is a vector that lies in a tensor product of vector spaces. The rank of a tensor T is the smallest integer r such that T can be written as a sum of r pure tensors. Finding such low rank decompositions of a tensor T is known as the PARAFAC model. This model has many applications: Algebraic Complexity Theory, Chemometrics, Neuroscience, Signal Processing to name a few. An alternative is the Convex Decomposition (CoDe) model. It uses the nuclear norm of tensors and is more numerically stable. We will discuss upper and lower bound for the rank and nuclear norm of some tensors of interest, and some applications.

Hosts: Jiawang Nie and Alireza Salehi Golsefidy

### June 2, 2016

### 4:00 PM

### AP&M 6402

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