Topics in Quaternion Linear Algebra / / Leiba Rodman.
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,...
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Rodman, Leiba, author. aut http://id.loc.gov/vocabulary/relators/aut Topics in Quaternion Linear Algebra / Leiba Rodman. Course Book Princeton, NJ : Princeton University Press, [2014] ©2014 1 online resource (384 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Princeton Series in Applied Mathematics ; 45 Frontmatter -- Contents -- Preface -- Chapter One. Introduction -- Chapter Two. The algebra of quaternions -- Chapter Three. Vector spaces and matrices: Basic theory -- Chapter Four. Symmetric matrices and congruence -- Chapter Five. Invariant subspaces and Jordan form -- Chapter Six. Invariant neutral and semidefinite subspaces -- Chapter Seven. Smith form and Kronecker canonical form -- Chapter Eight. Pencils of hermitian matrices -- Chapter Nine. Skewhermitian and mixed pencils -- Chapter Ten. Indefinite inner products: Conjugation -- Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution -- Chapter Twelve. Mixed matrix pencils: Nonstandard involutions -- Chapter Thirteen. Indefinite inner products: Nonstandard involution -- Chapter Fourteen. Matrix equations -- Chapter Fifteen. Appendix: Real and complex canonical forms -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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 It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Algebras, Linear Textbooks. Algebras, Linear. Quaternions Textbooks. Quaternions. MATHEMATICS / Algebra / Linear. bisacsh 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. Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package 9783110515831 ZDB-23-PAM Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 9783110665925 print 9780691161853 https://doi.org/10.1515/9781400852741?locatt=mode:legacy https://www.degruyter.com/isbn/9781400852741 Cover https://www.degruyter.com/document/cover/isbn/9781400852741/original |
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English |
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eBook |
author |
Rodman, Leiba, Rodman, Leiba, |
spellingShingle |
Rodman, Leiba, Rodman, Leiba, Topics in Quaternion Linear Algebra / Princeton Series in Applied Mathematics ; Frontmatter -- Contents -- Preface -- Chapter One. Introduction -- Chapter Two. The algebra of quaternions -- Chapter Three. Vector spaces and matrices: Basic theory -- Chapter Four. Symmetric matrices and congruence -- Chapter Five. Invariant subspaces and Jordan form -- Chapter Six. Invariant neutral and semidefinite subspaces -- Chapter Seven. Smith form and Kronecker canonical form -- Chapter Eight. Pencils of hermitian matrices -- Chapter Nine. Skewhermitian and mixed pencils -- Chapter Ten. Indefinite inner products: Conjugation -- Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution -- Chapter Twelve. Mixed matrix pencils: Nonstandard involutions -- Chapter Thirteen. Indefinite inner products: Nonstandard involution -- Chapter Fourteen. Matrix equations -- Chapter Fifteen. Appendix: Real and complex canonical forms -- Bibliography -- Index |
author_facet |
Rodman, Leiba, Rodman, Leiba, |
author_variant |
l r lr l r lr |
author_role |
VerfasserIn VerfasserIn |
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Rodman, Leiba, |
title |
Topics in Quaternion Linear Algebra / |
title_full |
Topics in Quaternion Linear Algebra / Leiba Rodman. |
title_fullStr |
Topics in Quaternion Linear Algebra / Leiba Rodman. |
title_full_unstemmed |
Topics in Quaternion Linear Algebra / Leiba Rodman. |
title_auth |
Topics in Quaternion Linear Algebra / |
title_alt |
Frontmatter -- Contents -- Preface -- Chapter One. Introduction -- Chapter Two. The algebra of quaternions -- Chapter Three. Vector spaces and matrices: Basic theory -- Chapter Four. Symmetric matrices and congruence -- Chapter Five. Invariant subspaces and Jordan form -- Chapter Six. Invariant neutral and semidefinite subspaces -- Chapter Seven. Smith form and Kronecker canonical form -- Chapter Eight. Pencils of hermitian matrices -- Chapter Nine. Skewhermitian and mixed pencils -- Chapter Ten. Indefinite inner products: Conjugation -- Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution -- Chapter Twelve. Mixed matrix pencils: Nonstandard involutions -- Chapter Thirteen. Indefinite inner products: Nonstandard involution -- Chapter Fourteen. Matrix equations -- Chapter Fifteen. Appendix: Real and complex canonical forms -- Bibliography -- Index |
title_new |
Topics in Quaternion Linear Algebra / |
title_sort |
topics in quaternion linear algebra / |
series |
Princeton Series in Applied Mathematics ; |
series2 |
Princeton Series in Applied Mathematics ; |
publisher |
Princeton University Press, |
publishDate |
2014 |
physical |
1 online resource (384 p.) Issued also in print. |
edition |
Course Book |
contents |
Frontmatter -- Contents -- Preface -- Chapter One. Introduction -- Chapter Two. The algebra of quaternions -- Chapter Three. Vector spaces and matrices: Basic theory -- Chapter Four. Symmetric matrices and congruence -- Chapter Five. Invariant subspaces and Jordan form -- Chapter Six. Invariant neutral and semidefinite subspaces -- Chapter Seven. Smith form and Kronecker canonical form -- Chapter Eight. Pencils of hermitian matrices -- Chapter Nine. Skewhermitian and mixed pencils -- Chapter Ten. Indefinite inner products: Conjugation -- Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution -- Chapter Twelve. Mixed matrix pencils: Nonstandard involutions -- Chapter Thirteen. Indefinite inner products: Nonstandard involution -- Chapter Fourteen. Matrix equations -- Chapter Fifteen. Appendix: Real and complex canonical forms -- Bibliography -- Index |
isbn |
9781400852741 9783110515831 9783110665925 9780691161853 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA196 |
callnumber-sort |
QA 3196 |
url |
https://doi.org/10.1515/9781400852741?locatt=mode:legacy https://www.degruyter.com/isbn/9781400852741 https://www.degruyter.com/document/cover/isbn/9781400852741/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
512 - Algebra |
dewey-full |
512.5 |
dewey-sort |
3512.5 |
dewey-raw |
512.5 |
dewey-search |
512.5 |
doi_str_mv |
10.1515/9781400852741?locatt=mode:legacy |
oclc_num |
881568749 |
work_keys_str_mv |
AT rodmanleiba topicsinquaternionlinearalgebra |
status_str |
n |
ids_txt_mv |
(DE-B1597)447973 (OCoLC)881568749 |
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cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2014-2015 |
is_hierarchy_title |
Topics in Quaternion Linear Algebra / |
container_title |
Title is part of eBook package: De Gruyter Princeton Series in Applied Mathematics eBook-Package |
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