Consider the vectors in C? (sometimes called spinors) ' (cos(0/2)e-ie/2 sin(0/2)e-i+/2 - cos(8/2)e**/2 V2 sin(0/2)e*6/2 (i) First show that they are normalized and orthonormal. (ii) Assume that for the vector vị is an eigenvector with the corresponding eigenvalue +1 and that the vector v2 is an eigenvector with the corresponding eigenvalue -1. Apply the spectral theorem to find the corresponding 2 x 2 matrix. (iii) Since the vectors vị and v2 form an orthonormal basis in C2 we can form an orthonormal basis in C4 via the Kronecker product W11 = V1 ® v1, W12 = V1 8 V2, W21 = V2 ® v1, W22 = V2 8 V2. Assume that the eigenvalue for w11 is +1, for w12 -1, for W21 -1 and for w22 +1. Apply the spectral theorem to find the corresponding 4 x 4 matrix.

Consider the vectors in C? (sometimes called spinors) ' (cos(0/2)e-ie/2 sin(0/2)e-i+/2 - cos(8/2)e**/2 V2 sin(0/2)e*6/2 (i) First show that they are normalized and orthonormal. (ii) Assume that for the vector vị is an eigenvector with the corresponding eigenvalue +1 and that the vector v2 is an eigenvector with the corresponding eigenvalue -1. Apply the spectral theorem to find the corresponding 2 x 2 matrix. (iii) Since the vectors vị and v2 form an orthonormal basis in C2 we can form an orthonormal basis in C4 via the Kronecker product W11 = V1 ® v1, W12 = V1 8 V2, W21 = V2 ® v1, W22 = V2 8 V2. Assume that the eigenvalue for w11 is +1, for w12 -1, for W21 -1 and for w22 +1. Apply the spectral theorem to find the corresponding 4 x 4 matrix.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 8E

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