Show that if A and B are matrices which don’t commute, then eA+B = eAeB, but if they do commute then the relation holds. Hint: Write out several terms of the infinite series for eA, eB, and eA+B and do the multiplications carefully assuming that A and B don’t commute. Then see what happens if they do commute.

Show that if A and B are matrices which don’t commute, then eA+B = eAeB, but if they do commute then the relation holds. Hint: Write out several terms of the infinite series for eA, eB, and eA+B and do the multiplications carefully assuming that A and B don’t commute. Then see what happens if they do commute.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter6: Some Methods In The Calculus Of Variations

Section: Chapter Questions

Problem 6.15P

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Show that if A and B are matrices which don’t commute, then e^A+^B = eAeB, but if they do commute then the relation holds. Hint: Write out several terms of the infinite series for e^A, e^B, and e^A+^B and do the multiplications carefully assuming that A and B don’t commute. Then see what happens if they do commute.

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