Obtain the corresponding normalized eigenvectors

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Question 1:

Consider the matrix A given by

715_Matrix.jpg

(a) calculate eigenvalues λ1 and λ2 and obtain the corresponding normalized eigenvectors v^1 and v^2 for A. It should be apparent at the outset, from the structure of A, that the eigenvectors may realized as an orthonormal set. Why?

(b) Show by direct calculation that A may be written as

A = U†DU 

where U is a unitary matrix and D is a matrix with nonzero entries only on the main diagonal.

463_Matrix1.jpg

Question 2:

Use the results of 1) to show that

1019_Matrix2.jpg

where cosh(x) = (ex + e-x)/2 and sinh(x) = (ex - e-x)/2.

Reference no: EM131572477

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