Let A be an nxn matrix and v is an eigenvector of A corresponding to the eigenvalue A. Show that (a) - Jv is an eigenvector of the matrix B = A – cl. (I is the identity matrix) corresponding to the eigenvalue A-c, for any scalar c. (b) | If A = c is an eigenvalue of A, then O is an eigenvalue of B = A- c.

Let A be an nxn matrix and v is an eigenvector of A corresponding to the eigenvalue A. Show that (a) - Jv is an eigenvector of the matrix B = A – cl. (I is the identity matrix) corresponding to the eigenvalue A-c, for any scalar c. (b) | If A = c is an eigenvalue of A, then O is an eigenvalue of B = A- c.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 24EQ

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