eBook

Topics in Quaternion Linear Algebra

Rodman, Leiba

2014

Overview

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 It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and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.

• Publisher: Princeton University Press
• Subject: Addition / Algebra / Algebra & number theory / Algebraic equation / Algebraic Riccati equation / Algebras, Linear / Algebras, Linear -- Textbooks / Applied mathematics / Automorphism / Boundedness / Calculus, Science / Canonical form / Clifford algebra / Coefficient / Compact space / Companion matrix / Complex Analysis, PBF, PBK, PBKD, UY, PH, TBC / Complex number / Computation / Computer Science, Mathematics / Convex set / Determinant / Diagonal matrix / Diagonalizable matrix / Dimension (vector space) / Direct sum / Division algebra / Division by zero / Division ring / Eigenvalues and eigenvectors / Endomorphism / Engineering (General), Mathematics / Equation / Equivalence class / Existential quantification / Factorization / General Topics for Engineers / General, Technology & Engineering / Hamiltonian matrix / Hermitian matrix / Invariant subspace / Invertible matrix / Jordan normal form / Linear algebra / Linear combination / Linear differential equation / Linear independence / Linear map / Linear, Computers / Lipschitz continuity / Main diagonal / Mathematical induction / MATHEMATICS / MATHEMATICS / Algebra / General / MATHEMATICS / General / MATHEMATICS / Mathematical Analysis / Matrix (mathematics) / Matrix decomposition / Matrix pencil / Matrix polynomial / Matrix representation / Metric space / Natural number / Numerical range / Open problem / Orthogonality / Permutation / Physics / Polynomial / Positive real numbers / Positive semidefinite / Projection (linear algebra) / Quaternion / Quaternion algebra / Quaternions / Quaternions -- Textbooks / Real number / Scalar multiplication / SCIENCE / Physics / General / Scientific notation / Square root / Summation / Symmetric matrix / Symplectic vector space / Technology / Textbooks / Theorem / Triangular matrix / Vector space / Without loss of generality
• ISBN: 1400852749, 9781400852741, 0691161852, 9780691161853