(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I attached the problem in a picture so its easier to see.

2. Relevant equations

3. The attempt at a solution

These are the values i got

[tex]\lambda[/tex]_ 1 = 1

[tex]\lambda[/tex]_ 2 = -1

x_1 = [-i; 1] (x_1)^H = [i 1]

x_2 = [ i; 1] (x_2)^H = [-i 1]

* where x_1 and x_2 are 2x1 matricies, and their hermitians are 1x2

after each multiplication I got

[tex]\lambda[/tex]_ 1 x_1 (x_1)^H =

[1 -i

i 1]

[tex]\lambda[/tex]_ 2 x_2 (x_2)^H =

[-1 -i

i -1]

When I add these together I get

[0 -2i

2i 0]

which is not the original A_5. I can't figure out where I went wrong in this process. If someone could look over it and let me know that would be great. Thank you

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# Linear algebra - eigenvalues and eigenvectors and hermitian

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