.. 5. Let o1, 02, 03 be the Pauli spin matricesn-(: ¿). n-(: 3). -(; :)0 11 0103 =01iand oo = I2. Consider the vector space of 2 x 2 matrices over C.(i) Show that the 2 x 2 matrices11I2,1031are linearly independent.(ii) Show that any 2 x 2 complex matrix has a unique representation of the formaoI2 + ia101 + ia202 + ia303for some ao, a1, a2, a3 € C.

Answered: Image /qna-images/answer/503a383d-770a-462b-9f0b-cce87d8e9b0e.jpg

5. Let o1, 02, 03 be the Pauli spin matrices 0 1 1 0 1 03 = 01 02 i and oo = I2. Consider the vector space of 2 x 2 matrices over C. (i) Show that the 2 x 2 matrices 1 1 12, 1 03 1 are linearly independent. (ii) Show that any 2x 2 complex matrix has a unique representation of the form aoI2 + ia101 + ia202 + ia303 for some ao, a1, a2, a3 € C.

5. Let o1, 02, 03 be the Pauli spin matrices 0 1 1 0 1 03 = 01 02 i and oo = I2. Consider the vector space of 2 x 2 matrices over C. (i) Show that the 2 x 2 matrices 1 1 12, 1 03 1 are linearly independent. (ii) Show that any 2x 2 complex matrix has a unique representation of the form aoI2 + ia101 + ia202 + ia303 for some ao, a1, a2, a3 € C.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 24E

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