##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Xinzhen Zhang

#### UCSD

## Rank Decomposition of Symmetric Tensor

##### Abstract:

In this talk, it is shown that a rank decomposition of symmetric tensors must be its symmetric rank decomposition when the tensor's rank is less than its order. Furthermore, when the rank of symmetric tensors equals the order, the symmetric rank must be the rank. As a corollary, for symmetric tensors, rank and symmetric rank coincide when rank is at most order. This partially gives a positive answer to the Comon's conjecture. Finally, a sufficient condition under which a symmetric decomposition of symmetric tensors is a symmetric rank decomposition is presented. Some examples are presented to show the efficiency of the condition.

### December 2, 2014

### 10:00 AM

### AP&M 2402

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