Orthogonal Decomposition of Symmetric Tensors

Elina Robeva

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arXiv · 1409.6685

Orthogonal Decomposition of Symmetric Tensors

Elina Robeva

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Abstract

A real symmetric tensor is orthogonally decomposable (or odeco) if it can be written as a linear combination of symmetric powers of $n$ vectors which form an orthonormal basis of $\mathbb R^n$. Motivated by the spectral theorem for real symmetric matrices, we study the properties of odeco tensors. We give a formula for all of the eigenvectors of an odeco tensor. Moreover, we formulate a set of polynomial equations that vanish on the odeco variety and we conjecture that these polynomials generate its prime ideal. We prove this conjecture in some cases and give strong evidence for its overall correctness.

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BibTeX RIS

Elina Robeva. 2014-09-23. Orthogonal Decomposition of Symmetric Tensors. https://arxiv.org/abs/1409.6685

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