Question
Asked Oct 3, 2019
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Consider the following Hermitian matrix
3 1 i
2
1i
a)
find the eigenvalues
find the eigenvectors
b)
show that the eigenvectors are
c)
orthogonal (Le. perpendicular)
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Consider the following Hermitian matrix 3 1 i 2 1i a) find the eigenvalues find the eigenvectors b) show that the eigenvectors are c) orthogonal (Le. perpendicular)

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Expert Answer

Step 1

(a)

The eigen values is,

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3— 2 1-і =0 1 2-2) (3-2)(2-2)-(1-)1+i)=0 6-31-22+2-(1+i-i-?)=0

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Step 2

Solve the above relation.

Solve for the eigen values.

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6-52 2-(1+1= 0 6-52 22-2 0 22-52+4=0 22-2-42 4 0 2(2-1)-4(-1) 0 2= 4,1

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Step 3

(b)

Solve for eigen vector of the eige...

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(4-41)x 0 3-4 1-1i= 0 2-4 x, 1 -1 1-ix = 0 1 i-2 Jx (1)x -x = 0 (1+i)x -2x2

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