Journal of elasticity and the physical science of solids

, Volume 66, Issue 2, pp 159–169

On the Explicit Determination of the Polar Decomposition in n-Dimensional Vector Spaces

Authors

  • C.S. Jog
    • Department of Mechanical Engineering, Indian Institute of Science
Article

DOI: 10.1023/A:1021253906202

Cite this article as:
Jog, C. Journal of Elasticity (2002) 66: 159. doi:10.1023/A:1021253906202

Abstract

A method for the explicit determination of the polar decomposition (and the related problem of finding tensor square roots) when the underlying vector space dimension n is arbitrary (but finite), is proposed. The method uses the spectral resolution, and avoids the determination of eigenvectors when the tensor is invertible. For any given dimension n, an appropriately constructed van der Monde matrix is shown to play a key role in the construction of each of the component matrices (and their inverses) in the polar decomposition.

polar decompositionsquare roots of tensorsexplicit determination

Copyright information

© Kluwer Academic Publishers 2002