Linear Algebra over Division Ring (Russian Edition): System of Linear Equations - Softcover

Kleyn, Aleks

Softcover

ISBN 10: 1502982471 ISBN 13: 9781502982476

Publisher: CreateSpace Independent Publishing Platform, 2014

Synopsis

In this book I treat linear algebra over division ring. A system of linear equations over a division ring has properties similar to properties of a system of linear equations over a field. However, noncommutativity of a product creates a new picture. Matrices allow two products linked by transpose. Biring is algebra which defines on the set two correlated structures of the ring. As in the commutative case, solutions of a system of linear equations build up right or left vector space depending on type of system. We study vector spaces together with the system of linear equations because their properties have a close relationship. As in a commutative case, the group of automorphisms of a vector space has a single transitive representation on a basis manifold. This gives us an opportunity to introduce passive and active representations. Studying a vector space over a division ring uncovers new details in the relationship between passive and active transformations, makes this picture clearer.

Edition details

• Publisher: CreateSpace Independent Publishing Platform
• Publication date: 2014
• Language: Russian
• ISBN 10: 1502982471
• ISBN 13: 9781502982476
• Binding: Paperback
• Number of pages: 68