Topics in Quaternion Linear Algebra
By Leiba Rodman. 2014
302 citations recorded by the source corpus.
Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses or as a basis for a graduate course in linear algebra. The open problems can serve as research projects for undergraduates, topics for graduate students, or problems to be tackled by professional research mathematicians. The book is also an invaluable reference tool for researchers in fields where techniques based on quaternion analysis are used.
Subfields: Applied Mathematics, Computational Theory and Mathematics
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Citations in the corpus
- Eigenvalues and Singular Values of Dual Quaternion Matrices (2021, background): “If some entries of A cannot be observed, how can we recover these entries with an approximate m × n dual quaternion matrix B of a low “rank”? Unlike real matrices, or complex matrices, or even quaternion matrices [8, 10, 11], which have matured matrix theories, there is a blank on the dual quaternio”
- The general $\phi$-Hermitian solution to mixed pairs of quaternion matrix Sylvester equations (2017, methodology): “[27] Let φ be an anti-endomorphism of H.”