We define a linear bijection, h, between R4 and H(2), the set of complex 2 x 2 hermitian matrices, by t+x y – iz y + iz t- x (t, x, y, z) → We denote the matrix on the right-hand side by H. (i) Show that the matrix can be written as a linear combination of the Pauli spin matrices 01, 02, 03 and the identity matrix I2. (ii) Find the inverse map. (iii) Calculate the determinant of 2 x 2 hermitian matrix H. Discuss.

We define a linear bijection, h, between R4 and H(2), the set of complex 2 x 2 hermitian matrices, by t+x y – iz y + iz t- x (t, x, y, z) → We denote the matrix on the right-hand side by H. (i) Show that the matrix can be written as a linear combination of the Pauli spin matrices 01, 02, 03 and the identity matrix I2. (ii) Find the inverse map. (iii) Calculate the determinant of 2 x 2 hermitian matrix H. Discuss.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.1: Operations With Matrices

Problem 77E

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