proof that exp^(x+y) is not equal with
(exp^x)(exp^y)

given x and y is matrix
and xy is not equal to yx

please help

Question

proof that exp^(x+y) is not equal with 
(exp^x)(exp^y)

given x and y is matrix 
and xy is not equal to yx

please help

anonymous · Answer

go to this @diran http://en.wikipedia.org/wiki/Matrix_exponential

anonymous · Answer

may i know k is stand for?

fwizbang · Answer

Construct a counter example with x = ( 1 0    and y = (0 1
                                                         0 -1)                 1 0).

Since x^2 =y^2 =1, and (x+y)^2 = 2, you can evaluate all the exponential explicitly
via Taylor series expansions.