A linear transformation T is said to be nilpotent if T" = 0 for some n. Show that a nilpotent transformation is diagonalisable if and only if it is the 0 linear transformation.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.1: Introduction To Linear Transformations
Problem 39E: For the linear transformation from Exercise 33, find a T(1,1), b the preimage of (1,1), and c the...
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A linear transformation T is said to
be nilpotent if T"
0 for some n.
Show that a nilpotent
transformation is diagonalisable if
and only if it is the 0 linear
transformation.
Transcribed Image Text:A linear transformation T is said to be nilpotent if T" 0 for some n. Show that a nilpotent transformation is diagonalisable if and only if it is the 0 linear transformation.
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