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Root Preserving Transformations of Polynomials

by Branko Ćurgus (Western Washington University) and Vania Mascioni (Ball State Uniuversity)

This article originally appeared in:
Mathematics Magazine
April, 2007

Subject classification(s): Algebra and Number Theory | Linear Algebra | Linear Transformations


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?


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