Topics in quaternion linear algebra

Topics in quaternion linear algebra /

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Bibliographic Details
Main Author: Rodman, L. (Author)
Corporate Author: Ebooks Corporation
Format: Electronic eBook
Language:English
Published: Princeton : Princeton University Press, [2014]
Series:Princeton series in applied mathematics.
Subjects:
Algebras, Linear > Textbooks.
Quaternions > Textbooks.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

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245 1 0 |a Topics in quaternion linear algebra /  |c Leiba Rodman. 
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264 4 |c ©2014 
300 |a 1 online resource (xii, 363 pages.) 
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533 |a Electronic reproduction.  |b Perth, W.A.  |n Available via World Wide Web. 
588 0 |a Print version record. 
505 0 0 |a Machine generated contents note:   |g 1.  |t Introduction --   |g 1.1.  |t Notation and conventions --   |g 1.2.  |t Standard matrices --   |g 2.  |t algebra of quaternions --   |g 2.1.  |t Basic definitions and properties --   |g 2.2.  |t Real linear transformations and equations --   |g 2.3.  |t Sylvester equation --   |g 2.4.  |t Automorphisms and involutions --   |g 2.5.  |t Quadratic maps --   |g 2.6.  |t Real and complex matrix representations --   |g 2.7.  |t Exercises --   |g 2.8.  |t Notes --   |g 3.  |t Vector spaces and matrices: Basic theory --   |g 3.1.  |t Finite dimensional quaternion vector spaces --   |g 3.2.  |t Matrix algebra --   |g 3.3.  |t Real matrix representation of quaternions --   |g 3.4.  |t Complex matrix representation of quaternions --   |g 3.5.  |t Numerical ranges with respect to conjugation --   |g 3.6.  |t Matrix decompositions: nonstandard involutions --   |g 3.7.  |t Numerical ranges with respect to nonstandard involutions --   |g 3.8.  |t Proof of Theorem 3.7.5 --   |g 3.9.  |t metric space of subspaces --   |g 3.10.  |t Appendix: Multivariable real analysis --   |g 3.11.  |t Exercises --   |g 3.12.  |t Notes --   |g 4.  |t Symmetric matrices and congruence --   |g 4.1.  |t Canonical forms under congruence --   |g 4.2.  |t Neutral and semidefinite subspaces --   |g 4.3.  |t Proof of Theorem 4.2.6 --   |g 4.4.  |t Proof of Theorem 4.2.7 --   |g 4.5.  |t Representation of semidefinite subspaces --   |g 4.6.  |t Exercises --   |g 4.7.  |t Notes --   |g 5.  |t Invariant subspaces and Jordan form --   |g 5.1.  |t Root subspaces --   |g 5.2.  |t Root subspaces and matrix representations --   |g 5.3.  |t Eigenvalues and eigenvectors --   |g 5.4.  |t Some properties of Jordan blocks --   |g 5.5.  |t Jordan form --   |g 5.6.  |t Proof of Theorem 5.5.3 --   |g 5.7.  |t Jordan forms of matrix representations --   |g 5.8.  |t Comparison with real and complex similarity --   |g 5.9.  |t Determinants --   |g 5.10.  |t Determinants based on real matrix representations --   |g 5.11.  |t Linear matrix equations --   |g 5.12.  |t Companion matrices and polynomial equations --   |g 5.13.  |t Eigenvalues of hermitian matrices --   |g 5.14.  |t Differential and difference equations --   |g 5.15.  |t Appendix: Continuous roots of polynomials --   |g 5.16.  |t Exercises --   |g 5.17.  |t Notes --   |g 6.  |t Invariant neutral and semidefinite subspaces --   |g 6.1.  |t Structured matrices and invariant neutral subspaces --   |g 6.2.  |t Invariant semidefinite subspaces respecting conjugation --   |g 6.3.  |t Proof of Theorem 6.2.6 --   |g 6.4.  |t Unitary, dissipative, and expansive matrices --   |g 6.5.  |t Invariant semidefinite subspaces: Nonstandard involution --   |g 6.6.  |t Appendix: Convex sets --   |g 6.7.  |t Exercises --   |g 6.8.  |t Notes --   |g 7.  |t Smith form and Kronecker canonical form --   |g 7.1.  |t Matrix polynomials with quaternion coefficients --   |g 7.2.  |t Nonuniqueness of the Smith form --   |g 7.3.  |t Statement of the Kronecker form --   |g 7.4.  |t Proof of Theorem 7.3.2: Existence --   |g 7.5.  |t Proof of Theorem 7.3.2: Uniqueness --   |g 7.6.  |t Comparison with real and complex strict equivalence --   |g 7.7.  |t Exercises --   |g 7.8.  |t Notes --   |g 8.  |t Pencils of hermitian matrices --   |g 8.1.  |t Canonical forms --   |g 8.2.  |t Proof of Theorem 8.1.2 --   |g 8.3.  |t Positive semidefinite linear combinations --   |g 8.4.  |t Proof of Theorem 8.3.3 --   |g 8.5.  |t Comparison with real and complex congruence --   |g 8.6.  |t Expansive and plus-matrices: Singular H --   |g 8.7.  |t Exercises --   |g 8.8.  |t Notes --   |g 9.  |t Skewhermitian and mixed pencils --   |g 9.1.  |t Canonical forms for skewhermitian matrix pencils --   |g 9.2.  |t Comparison with real and complex skewhermitian pencils --   |g 9.3.  |t Canonical forms for mixed pencils: Strict equivalence --   |g 9.4.  |t Canonical forms for mixed pencils: Congruence --   |g 9.5.  |t Proof of Theorem 9.4.1: Existence --   |g 9.6.  |t Proof of Theorem 9.4.1: Uniqueness --   |g 9.7.  |t Comparison with real and complex pencils: Strict equivalence --   |g 9.8.  |t Comparison with complex pencils: Congruence --   |g 9.9.  |t Proofs of Theorems 9.7.2 and 9.8.1 --   |g 9.10.  |t Canonical forms for matrices under congruence --   |g 9.11.  |t Exercises --   |g 9.12.  |t Notes --   |g 10.  |t Indefinite inner products: Conjugation --   |g 10.1.  |t H-hermitian and H-skewhermitian matrices --   |g 10.2.  |t Invariant semidefinite subspaces --   |g 10.3.  |t Invariant Lagrangian subspaces I --   |g 10.4.  |t Differential equations I --   |g 10.5.  |t Hamiltonian, skew-Hamiltonian matrices: Canonical forms --   |g 10.6.  |t Invariant Lagrangian subspaces II --   |g 10.7.  |t Extension of subspaces --   |g 10.8.  |t Proofs of Theorems 10.7.2 and 10.7.5 --   |g 10.9.  |t Differential equations II --   |g 10.10.  |t Exercises --   |g 10.11.  |t Notes --   |g 11.  |t Matrix pencils with symmetries: Nonstandard involution --   |g 11.1.  |t Canonical forms for ø-hermitian pencils --   |g 11.2.  |t Canonical forms for ø-skewhermitian pencils --   |g 11.3.  |t Proof of Theorem 11.2.2 --   |g 11.4.  |t Numerical ranges and cones --   |g 11.5.  |t Exercises --   |g 11.6.  |t Notes --   |g 12.  |t Mixed matrix pencils: Nonstandard involutions --   |g 12.1.  |t Canonical forms for ø-mixed pencils: Strict equivalence --   |g 12.2.  |t Proof of Theorem 12.1.2 --   |g 12.3.  |t Canonical forms of ø-mixed pencils: Congruence --   |g 12.4.  |t Proof of Theorem 12.3.1 --   |g 12.5.  |t Strict equivalence versus ø-congruence --   |g 12.6.  |t Canonical forms of matrices under ø-congruence --   |g 12.7.  |t Comparison with real and complex matrices --   |g 12.8.  |t Proof of Theorem 12.7.4 --   |g 12.9.  |t Exercises --   |g 12.10.  |t Notes --   |g 13.  |t Indefinite inner products: Nonstandard involution --   |g 13.1.  |t Canonical forms: Symmetric inner products --   |g 13.2.  |t Canonical forms: Skewsymmetric inner products --   |g 13.3.  |t Extension of invariant semidefinite subspaces --   |g 13.4.  |t Proofs of Theorems 13.3.3 and 13.3.4 --   |g 13.5.  |t Invariant Lagrangian subspaces --   |g 13.6.  |t Boundedness of solutions of differential equations --   |g 13.7.  |t Exercises --   |g 13.8.  |t Notes --   |g 14.  |t Matrix equations --   |g 14.1.  |t Polynomial equations --   |g 14.2.  |t Bilateral quadratic equations --   |g 14.3.  |t Algebraic Riccati equations --   |g 14.4.  |t Exercises --   |g 14.5.  |t Notes --   |g 15.  |t Appendix: Real and complex canonical forms --   |g 15.1.  |t Jordan and Kronecker canonical forms --   |g 15.2.  |t Real matrix pencils with symmetries --   |g 15.3.  |t Complex matrix pencils with symmetries. 
504 |a Includes bibliographical references and index. 
650 0 |a Algebras, Linear  |v Textbooks. 
650 0 |a Quaternions  |v Textbooks. 
710 2 |a Ebooks Corporation 
776 0 8 |i Print version:  |a Rodman, L.  |t Topics in quaternion linear algebra.  |d Princeton, New Jersey : Princeton University Press, [2014]  |z 9780691161853  |w (DLC) 2013050581 
830 0 |a Princeton series in applied mathematics. 
856 4 0 |u https://ebookcentral.proquest.com/lib/santaclara/detail.action?docID=1689375  |z Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)  |t 1 
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919 |a .ulebk  |b 2014-10-15 
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