[math-fun] exp(A)exp(B) = exp(A+B) = exp(B)exp(A)?
From: Dan Asimov <dasimov@earthlink.net> It's well known and easy to prove that if NxN matrices A and B commute, then (*) exp(A)exp(B) = exp(A+B) = exp(B)exp(A) But ... can happen if A,B do not commute... I think such examples of complex matrices are easier to come by than of real ones, so I'm particularly interested in the case where A and B are real.
-- 1. I point out, that any complex A,B example using nXn matrices, can immediately be converted to equivalent 2nX2n real matrices. 2. Initially I would suggest seeking upper triangular A,B.
A good start is the Baker-Campbell-Hausdorff formula: http://en.wikipedia.org/wiki/Baker%E2%80%93Campbell%E2%80%93Hausdorff_formul... On Tue, Aug 5, 2014 at 10:49 AM, Warren D Smith <warren.wds@gmail.com> wrote:
From: Dan Asimov <dasimov@earthlink.net> It's well known and easy to prove that if NxN matrices A and B commute, then (*) exp(A)exp(B) = exp(A+B) = exp(B)exp(A) But ... can happen if A,B do not commute... I think such examples of complex matrices are easier to come by than of real ones, so I'm particularly interested in the case where A and B are real.
-- 1. I point out, that any complex A,B example using nXn matrices, can immediately be converted to equivalent 2nX2n real matrices.
2. Initially I would suggest seeking upper triangular A,B.
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