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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.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the vectors in C2 (sometimes called spinors) :(cos(0/2)e-ie/2 sin(8/2)et*/2 sin(8/2)e-i$/2 ) . V2 - cos(8/2)e*#/2 (i) First show that they are normalized and orthonormal. (ii) Assume that for the vector vị is an eigenvector with the corresponding eigenvalue +1 and that the vector v2 is an eigenvector with the corresponding eigenvalue -1. Apply the spectral theorem to find the corresponding 2 x 2 matrix. (iii) Since the vectors vị and v2 form an orthonormal basis in C? we can form an orthonormal basis in C4 via the Kronecker product W11 = V1 ® V1, W12 = V1 ® v2, W21 = V2 ® V1, W22 = V2 ® V2. Assume that the eigenvalue for w11 is +1, for w12 –1, for w21 -1 and for w22 +1. Apply the spectral theorem to find the corresponding 4 x 4 matrix.
Transcribed Image Text:Consider the vectors in C2 (sometimes called spinors) :(cos(0/2)e-ie/2 sin(8/2)et*/2 sin(8/2)e-i$/2 ) . V2 - cos(8/2)e*#/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 C? we can form an orthonormal basis in C4 via the Kronecker product W11 = V1 ® V1, W12 = V1 ® v2, W21 = V2 ® V1, W22 = V2 ® 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.
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