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).

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter11: Matrices And Determinants

Section11.CR: Chapter Review

Problem 8CC

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