Polar decompositions of quaternion matrices in indefinite inner product spaces

Gilbert J. Groenewald, Dawie B.Janse VAN RENSBURG, André C.M. Ran, Frieda Theron, Madelein VAN STRAATEN*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an H-polar decomposition are found. In the process, an equivalent to Witt’s theorem on extending H-isometries to H-unitary matrices is given for quaternion matrices.

Original languageEnglish
Pages (from-to)659-670
Number of pages12
JournalElectronic Journal of Linear Algebra
Early online date29 Oct 2021
Publication statusPublished - 2021

Bibliographical note

Funding Information:
†Department of Mathematics and Applied Mathematics, Research Focus: Pure and Applied Analytics, North-West University, Private Bag X6001, Potchefstroom 2520, South Africa (gilbert.groenewald@nwu.ac.za, dawie.jansevanrensburg@nwu.ac.za, frieda.theron@nwu.ac.za, madelein.vanstraaten@nwu.ac.za). Supported by a grant from DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS).

Publisher Copyright:
© 2021, International Linear Algebra Society. All rights reserved.


  • Extending isometries
  • H-polar decompositions
  • Indefinite inner product
  • Quaternion matrices
  • Square roots of matrices
  • Witt’s theorem


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