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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
Finitely Generated Abelian Groups and Similarity of Matrices Over a Field

Finitely Generated Abelian Groups and Similarity of Matrices Over a Field

Norman, Christopher

Paperback

Series: Springer Undergraduate Mathematics, Book 0

AlgebraProgramming

ISBN10: 1447127293
ISBN13: 9781447127291
Publisher: Springer Nature
Published: Jan 26 2012
Pages: 381
Weight: 1.22
Height: 0.81 Width: 6.14 Depth: 9.21
Language: English

At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form.

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