Eigenvalues and Singular Value Decomposition of Dual Complex Matrices

2021/10/05 by Liqun Qi, Qi, Liqun, Ziyan Luo +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2110.02050

openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce right eigenvalues and subeigenvalues for square dual complex matrices. An n × n dual complex Hermitian matrix has exactly n right eigenvalues and subeigenvalues, which are all real. The Hermitian matrix is positive semi-definite or definite if and only if all of its right eigenvalues and subeigenvalues are nonnegative or positive, respectively. A Hermitian matrix can be diagonalized if and only if it has no right subeigenvalues. Then we present the singular value decomposition for general dual complex matrices. The results are further extended to dual quaternion matrices.

Citations

• Quaternions and matrices of quaternions
• Hand-Eye Calibration Using Dual Quaternions

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