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Taming the UnknownA History of Algebra from Antiquity to the Early Twentieth Century$
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Victor J. Katz and Karen Hunger Parshall

Print publication date: 2014

Print ISBN-13: 9780691149059

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691149059.001.0001

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PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2020. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 19 February 2020

Understanding Polynomial Equations in n Unknowns

Understanding Polynomial Equations in n Unknowns

(p.335) 12 Understanding Polynomial Equations in n Unknowns
Taming the Unknown

Victor J. Katz

Karen Hunger Parshall

Princeton University Press

This chapter examines the search for simultaneous solutions which eventually led to the creation of whole new algebraic constructs over the course of the eighteenth and nineteenth centuries. The constructs in question were the determinants, matrices, and invariants, among others. These, like groups, came to define new algebraic areas of inquiry in and of themselves. They were borne through a protracted search over the latter half of the millennium for more general techniques for solving systems of equations simultaneously—an issue which has been coming up frequently in mathematical problems since ancient times. The chapter looks at the evolution of these constructs and how mathematicians had come ever closer to their ideal solution.

Keywords:   polynomial equations, n unknowns, simultaneous solutions, new algebraic constructs, determinants, matrices, invariants, linear equations, linear transformations

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