Find the eigenvalues A1 < A2 and associated orthonormal eigenvectors of the symmetric matrix -1 -3 -3 -1 A = -1 -3 -3 -1 -1/sqrt(2) O/sqrt(2) 1/sqrt(2) O/sqrt(2) -4 has associated orthonormal eigenvectors O/sqrt(2) -1/sqrt(2) O/sqrt(2) 1/sqrt(2) 1/sqrt(2) O/sqrt(2) 1/sqrt(2) O/sqrt(2) 2 has associated orthonormal eigenvectors O/sqrt(2) 1/sqrt(2) O/sqrt(2) 1/sqrt(2) Note: The eigenvectors above form an orthonormal eigenbasis for A. ||

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Q: Let's now find the corresponding eigenvectors: Plugging in a₁: Plugging in a2: 0 1 (9) 0 - 0 - λ 1 0…

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Q: Q5/ Find the eigenvalues for matrix A [1 0 -11 1 2 1 2 3 A= L2

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Q: "The eigen values of Hermitian operator are real. What you can say about eigen values"

A: Using the fact that Mij*=Mji , then we have  Mv→,v→=∑i∑jMijvj*vi=∑i∑jMjiv*j vi=∑j vj*∑iMijvi=v→,Mv→…

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