# 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