Solution Found!
A diagonal matrix like = 1 0 0 2 satisfies the usual rule e (t+T) = e t e T , because
Chapter 5, Problem 5.4.5(choose chapter or problem)
A diagonal matrix like = 1 0 0 2 satisfies the usual rule e (t+T) = e t e T , because the rule holds for each diagonal entry. (a) Explain why e A(t+T) = e Ate AT , using the formula e At = SetS 1 . (b) Show that e A+B = e A e B is not true for matrices, from the example A = " 0 0 1 0# B = " 0 1 0 0 # (use series for e A and e B ).
Questions & Answers
QUESTION:
A diagonal matrix like = 1 0 0 2 satisfies the usual rule e (t+T) = e t e T , because the rule holds for each diagonal entry. (a) Explain why e A(t+T) = e Ate AT , using the formula e At = SetS 1 . (b) Show that e A+B = e A e B is not true for matrices, from the example A = " 0 0 1 0# B = " 0 1 0 0 # (use series for e A and e B ).
ANSWER:Step 1 of 3
Exponential of a Matrix: The Exponential of a Matrix can be determined using the method of diagonalization of the matrix, in order to compute the Jordan form of the matrix whose exponential is needed.