Let a be a fixed unit length vector (A is in R^3). Define a linear transformation T: R^3 -> R^3 by T(x)=(a.x)a (a.x refers the dot product between a and x) Show that a is an eigenvector for T. What is the associated eigen value ? Find another eigenvalue different from the one generated by eigenvector a and justify your answer by showing that it's an eigenvalue for T

Let a be a fixed unit length vector (A is in R^3). Define a linear transformation T: R^3 -> R^3 by T(x)=(a.x)a (a.x refers the dot product between a and x) Show that a is an eigenvector for T. What is the associated eigen value ? Find another eigenvalue different from the one generated by eigenvector a and justify your answer by showing that it's an eigenvalue for T

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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