# Singular values of tensors are Lagrange multipliers

J. Graaf, de

## 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 Eindhoven Technische Universiteit Eindhoven 8 Published - 2011

### Publication series

Name CASA-report 1102 0926-4507

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