Polar decompositions of quaternion matrices in indefinite inner product spaces

2021/06/19 by G. J. Groenewald, Groenewald, G. J., D.B. Janse van Rensburg +7
Computer Science · Mathematics · #15A23 #15B33 #47B50 #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2106.10527

openalex publication_date 2021/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Quaternions and matrices of quaternions

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