Topics in Quaternion Linear Algebra

Leiba Rodman is professor of mathematics at the College of William & Mary. His books include Matrix Polynomials, Algebraic Riccati Equations, and Indefinite Linear Algebra and Applications.

One of Choice's Outstanding Academic Titles for 2015 "Rodman fills a void in the monographic literature with this work."--Choice "The book is self-contained and well organized... Full and detailed proofs are supplied. Another exciting point is the presence of many open problems throughout the book."--Gisele C. Ducati, MatchSciNet

• *FrontMatter, pg. i*Contents, pg. vii*Preface, pg. xi*Chapter One. Introduction, pg. 1*Chapter Two. The algebra of quaternions, pg. 9*Chapter Three. Vector spaces and matrices: Basic theory, pg. 28*Chapter Four. Symmetric matrices and congruence, pg. 64*Chapter Five. Invariant subspaces and Jordan form, pg. 83*Chapter Six. Invariant neutral and semidefinite subspaces, pg. 131*Chapter Seven. Smith form and Kronecker canonical form, pg. 153*Chapter Eight. Pencils of hermitian matrices, pg. 172*Chapter Nine. Skewhermitian and mixed pencils, pg. 194*Chapter Ten. Indefinite inner products: Conjugation, pg. 228*Chapter Eleven. Matrix pencils with symmetries: Nonstandard involution, pg. 261*Chapter Twelve. Mixed matrix pencils: Nonstandard involutions, pg. 279*Chapter Thirteen. Indefinite inner products: Nonstandard involution, pg. 300*Chapter Fourteen. Matrix equations, pg. 328*Chapter Fifteen. Appendix: Real and complex canonical forms, pg. 339*Bibliography, pg. 353*Index, pg. 361