Journal of elasticity and the physical science of solids

, Volume 66, Issue 2, pp 159-169

First online:

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

  • C.S. JogAffiliated withDepartment of Mechanical Engineering, Indian Institute of Science

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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 decomposition square roots of tensors explicit determination