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). If we can compute the eigenvalues of T to be 0 and 1, what would be the dimension of the eigenspaces corresponding with the found eigenvalues ? Is the standard matrix T diagonalizable ?

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). If we can compute the eigenvalues of T to be 0 and 1, what would be the dimension of the eigenspaces corresponding with the found eigenvalues ? Is the standard matrix T diagonalizable ?

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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