The discussion centers on the transformation of matrix addition into multiplication without using exponentiation. Participants clarify that while the equation e^{A+B} = e^A e^B holds true under the condition that matrices A and B commute (AB = BA), exponentiation leads to infinite results, unlike finite matrix multiplication. A proposed solution for expressing A.B in terms of exponentials is X = ABe^{-(A+B)}, although this approach is noted to be restrictive due to its lack of distributive properties.
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aliya said:Suppose two matrices A and B . i want to transform matrix addition to matrix multiplication. e.g A+B into A.B.
Can anybody please tell me of any way i can do it ,except exponentiation? exponentiation gives an infinite answer.
HallsofIvy said:It is certainly true that e^{A+ B}= e^Ae^B but what do you mean by "exponentiation gives an infinite answer"?
trambolin said:e^{A+ B}= e^Ae^B if and only if AB = BA
No, it doesn't. If A and B are n by n matrices, then so are e^A, e^B, and e^Ae^B.aliya said:Thankyou all for your replies.
"By exponentiation gives an infinite answer" i meant that suppose two matrices A and B, their multiplication A.B gives a finite answer i.e another finite matrix. but e^A.e^B give an infinite answer. doesn't it?
Also can you please tell if there exists any X such that A.B=X(e^A.e^B)?