Linear algebra: Let A = G) (1) Find the eigenvalues and the corresponding normalised eigenvectors

Linear algebra: Let A = G) (1) Find the eigenvalues and the corresponding normalised eigenvectors. Show that the eigenvectors are mutually orthogonal and satisfy the completeness relation

1. Find the unitary matrix U that diagonalises A according to UTAU = = ( ).
(2) where Ip are the eigenvalues of A.
(b) Tensor product and entanglement: the state |4) = 72(100) + |11)) is an example of an entangled state of two spin-1/2 particles. Show that the two-particle state ) cannot be expressed as a tensor product of two single particle states.
(c) (Hermitian conjugation: the adjoint (Hermitian conjugate) B = At of a linear operator A is defined by (B$|) = (Av). Use this definition to calculate the adjoint of (a) (Bl.


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