An n x n matrix A is called nilpotent if there is a positive integer k such that Ak = 0. Show that a nonzero nilpotent matrix is not diagonalizable. [Hint: if A is diagonalizable then P-¹APD where P is invertible and D is a diagonal matrix. Solve this for. A and raise to power k. ] =
An n x n matrix A is called nilpotent if there is a positive integer k such that Ak = 0. Show that a nonzero nilpotent matrix is not diagonalizable. [Hint: if A is diagonalizable then P-¹APD where P is invertible and D is a diagonal matrix. Solve this for. A and raise to power k. ] =
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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