(i) Let H be an nxn matrix over C. Assume that H is hermitian and unitary. What can be said about the eigenvalues of H? (ii) An n x n matrix A such that A2 = A is called idempotent. What can be said about the eigenvalues of such a matrix? (iii) An nx n matrix A for which AP = 0n, where p is a positive integer, is called nilpotent. What can be said about the eigenvalues of such a matrix? (iv) An n x n matrix A such that A? = In is called involutory. What can be said about the eigenvalues of such a matrix? %3D %3D

(i) Let H be an nxn matrix over C. Assume that H is hermitian and unitary. What can be said about the eigenvalues of H? (ii) An n x n matrix A such that A2 = A is called idempotent. What can be said about the eigenvalues of such a matrix? (iii) An nx n matrix A for which AP = 0n, where p is a positive integer, is called nilpotent. What can be said about the eigenvalues of such a matrix? (iv) An n x n matrix A such that A? = In is called involutory. What can be said about the eigenvalues of such a matrix? %3D %3D

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 41EQ

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