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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Linear Algebra over Division Ring: System of Linear Equations

Linear Algebra over Division Ring: System of Linear Equations

Kleyn, Aleks

Paperback

Algebra

ISBN10: 147763181X
ISBN13: 9781477631812
Publisher: Createspace
Published: Jun 16 2012
Pages: 62
Weight: 0.27
Height: 0.16 Width: 7.00 Depth: 10.00
Language: English
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 frame 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.

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