Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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.

Elementary Linear Algebra (MindTap Course List)
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
See similar textbooks
icon
Related questions
Question
..
5. Let o1, 02, 03 be the Pauli spin matrices n-(: ¿). n-(: 3). -(; :) 0 1 1 0 1 03 = 01 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 I2, 1 03 1 are linearly independent. (ii) Show that any 2 x 2 complex matrix has a unique representation of the form aoI2 + ia101 + ia202 + ia303 for some ao, a1, a2, a3 € C.
Transcribed Image Text:5. Let o1, 02, 03 be the Pauli spin matrices n-(: ¿). n-(: 3). -(; :) 0 1 1 0 1 03 = 01 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 I2, 1 03 1 are linearly independent. (ii) Show that any 2 x 2 complex matrix has a unique representation of the form aoI2 + ia101 + ia202 + ia303 for some ao, a1, a2, a3 € C.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:
9781305658004
Author:
Ron Larson
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS