Question
Asked Oct 8, 2019
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Show that if AB
BA, then eA+BeAe, but if they do commute, then the relations hold. Hint:
Write out several terms for e4+B, e4, e and do the multiplication carefully
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Show that if AB BA, then eA+BeAe, but if they do commute, then the relations hold. Hint: Write out several terms for e4+B, e4, e and do the multiplication carefully

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Expert Answer

Step 1

The problem concerns the commutativity properties of the exponentials of square matrices

Step 2

Definition of e^X= exp(X), X a square matrix

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X" . (by definition) n!

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Step 3

Consider e^(A+B) and e^A times...

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(A+B) (by definition). 4+B n! =I+ (A+B)+ (4+ B)? 2! +.. AAB+BA+B =I+(A+B) +., (1) 2!

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