On left eigenvalues of a quaternionic matrix

By Liping Huang, Wasin So. 2001

111 citations recorded by the source corpus.

Abstract In this paper, we introduce the concept of left and right eigenvalues for a quaternionic matrix, and investigate their properties, quantities and relationship.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/b160494d651dbca81ec79642c97d54edabd8da4a

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In Applied Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Quaternion-MUSIC for vector-sensor array processing (2006, background): “However this is not the case for the left eigenvalues of quaternion matric es, as their existence is still problematic [35].”
Determinantal representations of the Moore–Penrose inverse over the quaternion skew field and corresponding Cramer's rules (2010, background): “The theory on the left eigenvalues of quaternion matrices has been investigated in particular in [9,15,18].”
On the eigenvalues of quaternion matrices (2011, background): “Huang and So [14] showed that in order for l (A) to be Linear and Multilinear Algebra 455”
Geršgorin type theorems for quaternionic matrices (2007, methodology): “Lemma 1 [13].”
Singular value decomposition of quaternion matrices: a new tool for vector-sensor signal processing (2004, background): “Important research works on this subject were carried out by Zhang [37], Huang and So [15], Thompson [32], among others.”
The Quaternion LMS Algorithm for Adaptive Filtering of Hypercomplex Processes (2009, background): “Furthermore, the left eigenvalue decomposition of a quaternion is still an ongoing research topic [44].”