Let A be an n x n matrix over C". Let A be an eigenvalue of A. A generalized eigenvector x € C" of A corresponding to the eigenvalue A is a nontrivial solution of (A – AIn)³ x = 0n for some j e {1,2,.}, where 0n is the n-dimensional zero vector. For j we find the eigenvectors. It follows that x is a generalized eigenvector of A corresponding to A if and only if (A – Am)" x = 0,. Find the eigenvectors and generalized eigenvectors of the nonnormal matrix 1 -1 0

Let A be an n x n matrix over C". Let A be an eigenvalue of A. A generalized eigenvector x € C" of A corresponding to the eigenvalue A is a nontrivial solution of (A – AIn)³ x = 0n for some j e {1,2,.}, where 0n is the n-dimensional zero vector. For j we find the eigenvectors. It follows that x is a generalized eigenvector of A corresponding to A if and only if (A – Am)" x = 0,. Find the eigenvectors and generalized eigenvectors of the nonnormal matrix 1 -1 0

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

See similar textbooks