Question
Asked Oct 8, 2019
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Consider the following Hermitian matrix
1 i
3
i
find the eigenvalues
a)
find the eigenvectors
b)
show that the eigenvectors are
c)
orthogonal (i.e. perpendicular)
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Consider the following Hermitian matrix 1 i 3 i find the eigenvalues a) find the eigenvectors b) show that the eigenvectors are c) orthogonal (i.e. perpendicular)

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Expert Answer

Step 1

To find the eigenvalues, eigenvectors and establish the required orthogonallity

Step 2

1) eigenvalues are found by solving the characxteristic equation of T

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1 -i 3 Let T = |1+i 2 Deigenvalues are roots of c2-tr(T)c+det(T) = 0 c2-5c+4 0c= 1,c =4

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Step 3

2) eigenvector for c =1 is the column ...

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1-i Let T |1+i 2 1)eigenvector for c 1 1-i 3 х х 2 x1y(1 i)

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