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Classifying Nilpotent Maps via Partition Diagrams

Nick Loehr
The College Mathematics Journal
Vol. 45, No. 2 (March 2014), pp. 108-115
DOI: 10.4169/college.math.j.45.2.108
Stable URL: http://www.jstor.org/stable/10.4169/college.math.j.45.2.108
Page Count: 8
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Classifying Nilpotent Maps via Partition Diagrams
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Abstract

Summary This note uses a visual analysis of partition diagrams to give an elementary, pictorial proof of the classification theorem for nilpotent linear maps. We show that any nilpotent map is represented by a matrix with ones in certain positions on the first super-diagonal and zeroes elsewhere.

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