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Root Preserving Transformations of Polynomials

The article answers negatively the question, “Is there a (non-trivial) linear transformation \(T\) from \(P_n\), the vector space of all polynomials of degree at most \(n\), to \(P_n\) such that for each \(p\) in \( P_n\) with a real or complex root, the polynomials \(p\) and \(T( p)\) have a common root?" The proof is based on the fact polynomials of degree at most \(n\) have at most \(n\) roots in the real or complex numbers. This article investigates an area common to algebra and linear algebra.

Old Node ID: 
3656
MSC Codes: 
15A04
Author(s): 
Branko Ćurgus (Western Washington University) and Vania Mascioni (Ball State Uniuversity)
Publication Date: 
Wednesday, April 13, 2011
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
April, 2007
Subject(s): 
Algebra and Number Theory
Linear Algebra
Linear Transformations
Topic(s): 
Linear Algebra
Linear Transformation
Vector Spaces, Subspaces
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Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
5.00
Rating Sum: 
15.00
Rating Average: 
3.00
Modify Date: 
Wednesday, April 13, 2011
Average: 3 (5 votes)

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