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7. Which of the following types of linear transformations are always diagonalisable? (a) The idempotent transformations, satisfying T2 = T. (b) The nilpotent transformations, having a power which is zero (c) The invertible linear transformations (d) The linear transformations whose minimal polynomial factors completely into distinct linear factors. (e) The self adjoint transformations on an inner product space.

7. Which of the following types of linear transformations are always diagonalisable? (a) The idempotent transformations, satisfying T2 = T. (b) The nilpotent transformations, having a power which is zero (c) The invertible linear transformations (d) The linear transformations whose minimal polynomial factors completely into distinct linear factors. (e) The self adjoint transformations on an inner product space.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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7. Which of the following types of linear transformations are always diagonalisable? (a) The idempotent transformations, satisfying T² = T. %3D (b) The nilpotent transformations, having a power which is zero (c) The invertible linear transformations (d) The linear transformations whose minimal polynomial factors completely into distinct linear factors. (e) The self adjoint transformations on an inner product space.
Transcribed Image Text:7. Which of the following types of linear transformations are always diagonalisable? (a) The idempotent transformations, satisfying T² = T. %3D (b) The nilpotent transformations, having a power which is zero (c) The invertible linear transformations (d) The linear transformations whose minimal polynomial factors completely into distinct linear factors. (e) The self adjoint transformations on an inner product space.
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