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Polynomial Translation Groups

Consider the vector space of polynomials of degree less than \(n\), and a polynomial \(p(x)\) in this space. The author describes the matrix \(M(r) \) that maps the polynomial \(p(x)\) to \(p(x+r)\), where \(r\) is a real number. The group structure of the matrices \(M(r)\) under multiplication then gives rise to various combinatorial identities.

Old Node ID: 
3501
MSC Codes: 
97G40, 15A04
Author(s): 
Dan Kalman (University of Wisconsin)
Publication Date: 
Sunday, June 27, 2010
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
January, 1983
Subject(s): 
Algebra and Number Theory
Linear Algebra
Matrix Algebra
Geometry and Topology
Plane Geometry
Transformations
Topic(s): 
Linear Algebra
Linear Transformation
Matrix Algebra
Matrix Multiplication
Flag for Digital Object Identifier: 
Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
120.00
Rating Sum: 
350.00
Rating Average: 
2.92
Applicable Course(s): 
3.8 Linear/Matrix Algebra
Modify Date: 
Sunday, June 27, 2010
Average: 2.9 (120 votes)

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