Show that if A is a diagonal matrix with diagonal elements a1, a2, . . . , an, then exp(At) is
also a diagonal matrix with diagonal elements exp(a1t), exp(a2t), . . . , exp(ant).

Question

Show that if A is a diagonal matrix with diagonal elements a1, a2, . . . , an, then exp(At) is
also a diagonal matrix with diagonal elements exp(a1t), exp(a2t), . . . , exp(ant).

anonymous · Answer

No idea what to do

phi · Answer

You can use the series expansion for e^x see https://en.wikipedia.org/wiki/Exponential_function#Formal_definition replace x with At in the series you need to show a diagonal matrix times itself gives a new diagonal matrix. because the series is the summation of powers of At (i.e. diagonal matrices), the sum of the series will be a diagonal matrix