### Abstract

This note has been inspired by the Masters Thesis of Femke van Belzen.
The Lagrange Multiplier Method is applied to construct a singular value decomposition
for Tensors in such a way that the number of zero terms in the 'Singular Value Expansion' is as large as possible.
The result is a bit disappointing in the sense that one would like to get 'a lot more' zeros in the q-dimensional number scheme of 'edge-length M', $q \geq 3$,which represents a q-tensor on a vector space of dimension M. It is shown that the maximum number of zeros one can get is $q dim SO(M) = \frac{q}{2} M(M-1)$. This number is significantly comparable with $M^q$ only if q = 2.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Technische Universiteit Eindhoven |

Number of pages | 8 |

Publication status | Published - 2011 |

### Publication series

Name | CASA-report |
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Volume | 1102 |

ISSN (Print) | 0926-4507 |

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## Cite this

Graaf, de, J. (2011).

*Singular values of tensors are Lagrange multipliers*. (CASA-report; Vol. 1102). Technische Universiteit Eindhoven.