Problem Let A1, A2, A3 be m x m matrices. Let B1, B2, B3 be n xn matrices. Consider the (n - m) x (n · m) matrices X1 = A1 ® In + Im ® B1, X2 = A2 ® In + Im ® B2, X3 = A3 ® In + Im ® B3. %3D (i) Calculate the commutators and show that the results can again be expressed using commutators. (ii) Assume that [41, A2] = A3, [A2, A3] = A1, [A3, A1] = A2 %3D and [В, В] 3 Вз, [Вә, Вз] 3 Ві, [Вз, B]] — Вz- [B3, B1] = B2. %3D %3D Use these commutation relations to simplify the results of (i).
Problem Let A1, A2, A3 be m x m matrices. Let B1, B2, B3 be n xn matrices. Consider the (n - m) x (n · m) matrices X1 = A1 ® In + Im ® B1, X2 = A2 ® In + Im ® B2, X3 = A3 ® In + Im ® B3. %3D (i) Calculate the commutators and show that the results can again be expressed using commutators. (ii) Assume that [41, A2] = A3, [A2, A3] = A1, [A3, A1] = A2 %3D and [В, В] 3 Вз, [Вә, Вз] 3 Ві, [Вз, B]] — Вz- [B3, B1] = B2. %3D %3D Use these commutation relations to simplify the results of (i).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Problem
Let A1, A2, A3 be m x m matrices. Let B1, B2, B3 be n xn
matrices. Consider the (n · m) × (n · m) matrices
X1 = A1 ® In + Im ® B1, X2 = A2 ® In + Im ® B2, X3 = A3 ® In + Im ® B3.
%3D
%3D
(i) Calculate the commutators and show that the results can again be expressed
using commutators.
(ii) Assume that
[41, A2] = A3, [A2, A3] = A1, [A3, A1] = A2
and
[B1, B2] = B3, [B2,B3] = B1, [B3, B1] = B2.
%3D
Use these commutation relations to simplify the results of (i).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F275f29ee-6496-43d8-8387-e0a575156ceb%2F1b9f9a9d-ae41-4ced-b3cc-66c3e2bb9d3a%2F2xefr3r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem
Let A1, A2, A3 be m x m matrices. Let B1, B2, B3 be n xn
matrices. Consider the (n · m) × (n · m) matrices
X1 = A1 ® In + Im ® B1, X2 = A2 ® In + Im ® B2, X3 = A3 ® In + Im ® B3.
%3D
%3D
(i) Calculate the commutators and show that the results can again be expressed
using commutators.
(ii) Assume that
[41, A2] = A3, [A2, A3] = A1, [A3, A1] = A2
and
[B1, B2] = B3, [B2,B3] = B1, [B3, B1] = B2.
%3D
Use these commutation relations to simplify the results of (i).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
