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The Invariant Theory of Matrices (University Lecture Series) (University Lecture, 69) free ebook download

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Mathematics

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Author(s):	Corrado De Concini

Date:	2021	Format:	pdf	Language:	English	ISBN/ASIN:	147044187X
Pages:	153	OCR:		Quality:		ISBN13:
Uploader:	maveriks	Upload Date:	8/2/2023 3:47:59 AM

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This book gives a unified, complete, and self-contained exposition of the main algebraic theorems of invariant theory for matrices in a characteristic free approach. More precisely, it contains the description of polynomial functions in several variables on the set of matrices with coefficients in an infinite field or even the ring of integers, invariant under simultaneous conjugation. Following Hermann Weyl's classical approach, the ring of invariants is described by formulating and proving (1) the first fundamental theorem that describes a set of generators in the ring of invariants, and (2) the second fundamental theorem that describes relations between these generators. The authors study both the case of matrices over a field of characteristic 0 and the case of matrices over a field of positive characteristic. While the case of characteristic 0 can be treated following a classical approach, the case of positive characteristic (developed by Donkin and Zubkov) is much harder. A presentation of this case requires the development of a collection of tools. These tools and their application to the study of invariants are exlained in an elementary, self-contained way in the book.
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Tags: Invariant Lecture Lecture Matrices Theory University University

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The Invariant Theory of Matrices (University Lecture Series) (University Lecture, 69) free ebook download

Category: Mathematics

Description: Click to see full description

Category:
Mathematics