0 iConsider the hermitian matrix M =-i 0 -iFind its eigenvalues,and verify that they are all real numbers, and in this case are distinct.Find eigenvectors for the three eigenvalues, and verify that they form anorthogonal set with respect to the standard inner product on C³.

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i Consider the hermitian matrix M -i 0 -i Find its eigenvalu i and verify that they are all real numbers, and in this case are distine Find eigenvectors for the three eigenvalues, and verify that they form

i Consider the hermitian matrix M -i 0 -i Find its eigenvalu i and verify that they are all real numbers, and in this case are distine Find eigenvectors for the three eigenvalues, and verify that they form

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.1: Inner Product Spaces

Problem 11AEXP

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Question

0 i
Consider the hermitian matrix M =
-i 0 -i
Find its eigenvalues,
and verify that they are all real numbers, and in this case are distinct.
Find eigenvectors for the three eigenvalues, and verify that they form an
orthogonal set with respect to the standard inner product on C³.

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