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Book
Topics in quaternion linear algebra
Author:
ISBN: 1400852749 Year: 2014 Publisher: Princeton, New Jersey ; Oxfordshire, England : Princeton University Press,

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Abstract

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 It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and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

Keywords

Algebras, Linear --- Quaternions --- Algebra, Universal --- Algebraic fields --- Curves --- Surfaces --- Numbers, Complex --- Vector analysis --- Linear algebra --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Cholesky factorization. --- Hamiltonian matrices. --- Jordan canonical form. --- Jordan form. --- Kronecker canonical form. --- Kronecker form. --- Kronecker forms. --- Schur triangularization theorem. --- Smith form. --- Sylvester equation. --- algebraic Riccati equations. --- antiautomorphisms. --- automorphisms. --- bilateral quadratic equations. --- boundedness. --- canonical forms. --- complex hermitian matrices. --- complex matric pencils. --- complex matrices. --- complex matrix polynomials. --- congruence. --- conjugation. --- conventions. --- determinants. --- diagonal form. --- diagonalizability. --- differential equations. --- dissipative matrices. --- eigenvalues. --- eigenvectors. --- equivalence. --- expansive matrices. --- hermitian inner product. --- hermitian matrices. --- hermitian matrix pencils. --- hermitian pencils. --- indefinite inner products. --- inertia theorems. --- invariant Langragian subspaces. --- invariant Langrangian subspaces. --- invariant neutral subspaces. --- invariant semidefinite subspaces. --- invariant subspaces. --- involutions. --- linear quadratic regulators. --- matrix algebra. --- matrix decompositions. --- matrix equations. --- matrix pencils. --- matrix polynomials. --- maximal invariant semidefinite subspaces. --- metric space. --- mixed matrix pencils. --- mixed pencils. --- mixed quaternion matrix pencils. --- neutral subspaces. --- nondegenerate. --- nonstandard involution. --- nonstandard involutions. --- nonuniqueness. --- notations. --- numerical cones. --- numerical ranges. --- pencils. --- polynomial matrix equations. --- quadratic maps. --- quaternion algebra. --- quaternion coefficients. --- quaternion linear algebra. --- quaternion matrices. --- quaternion matrix pencils. --- quaternion subspaces. --- quaternions. --- real linear transformations. --- real matrices. --- real matrix pencils. --- real matrix polynomials. --- real symmetric matrices. --- root subspaces. --- scalar quaternions. --- semidefinite subspaces. --- skew-Hamiltonian matrices. --- skewhermitian inner product. --- skewhermitian matrices. --- skewhermitian pencils. --- skewsymmetric matrices. --- square-size quaternion matrices. --- standard matrices. --- symmetric matrices. --- symmetries. --- symmetry properties. --- unitary matrices. --- vector spaces.


Multi
Topics in quaternion linear algebra
Author:
ISBN: 9781400852741 9780691161853 1400852749 Year: 2014 Publisher: Princeton, New Jersey ; Oxfordshire, England : Princeton University Press,

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Abstract

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.


Book
Matrix polynomials
Authors: --- ---
ISBN: 012287160X 9780122871603 Year: 1982 Publisher: New York ; London ; Paris : Academic Press,

Invariant subspaces of matrices with applications
Authors: --- ---
ISBN: 0471842605 9780471842606 Year: 1986 Publisher: New York (N.Y.): Wiley,


Book
Matrix polynomials
Authors: --- ---
ISBN: 9780898716818 0898716810 Year: 2009 Publisher: Philadelphia: Society for industrial and applied mathematics,

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Matrices

Matrices and indefinite scalar products
Authors: --- ---
ISBN: 376431527X Year: 1983 Publisher: Basel Birkhäuser

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Book
Advances in structured operator theory and related areas : the Leonid Lerer anniversary volume
Authors: --- ---
ISSN: 02550156 ISBN: 3034806388 3034807988 3034806396 Year: 2013 Volume: v. 237 Publisher: New York : Springer,

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This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer’s research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia type results, matrix polynomials, and related areas in operator and matrix theory. Biographical material  and Lerer's list of publications complete the volume.


Multi
Advances in structured operator theory and related areas : the Leonid Lerer anniversary volume
Authors: --- ---
ISSN: 02550156 ISBN: 9783034806398 3034806396 Year: 2013 Volume: v. 237 Publisher: New York : Springer,

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Abstract

This volume is dedicated to Leonid Lerer on the occasion of his seventieth birthday. The main part presents recent results in Lerer’s research area of interest, which includes Toeplitz, Toeplitz plus Hankel, and Wiener-Hopf operators, Bezout equations, inertia type results, matrix polynomials, and related areas in operator and matrix theory. Biographical material  and Lerer's list of publications complete the volume.


Book
Analysis of fluorinated polyimides flown on the Materials International Space Station Experiment
Authors: --- --- --- ---
Year: 2015 Publisher: Huntsville, Alabama : National Aeronautics and Space Administration, Marshall Space Flight Center,

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Contributions to operator theory and its applications : proceedings of the conference on operator theory and functional analysis, Mesa, Arizona, June 11-14, 1987
Authors: --- --- ---
ISBN: 9780817622213 0817622217 Year: 1988 Publisher: Basel: Birkhäuser,

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