# 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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Rating Count:
5.00
Rating Sum:
15.00
Rating Average:
3.00
Modify Date:
Wednesday, April 13, 2011